416.sagews

sage: bernoulli = lambda x : x^2
sage: bernoulli(6)
sage: eval('bernoulli(6)')
sage: sage_eval('1/bernoulli(6)')

42

sage: bernoulli = lambda x : x^2
sage: bernoulli(n)
sage: eval('bernoulli(n)')
sage: [sage_eval('bernoulli(n)')  for n in xrange(0, 50)] #

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/10.py", line 10, in <module> exec compile(ur'[sage_eval(\u0027bernoulli(n)\u0027) for n in xrange(_sage_const_0 , _sage_const_50 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/misc/sage_eval.py", line 199, in sage_eval return eval(source, sage.all.__dict__, locals) File "<string>", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 237, in bernoulli n = Integer(n) File "integer.pyx", line 601, in sage.rings.integer.Integer.__init__ (sage/rings/integer.c:6814) TypeError: unable to coerce <type 'function'> to an integer

sage: [next_prime(n)*n^2 for n in xrange(0, 50)] #nnnnnnn

[0, 2, 12, 45, 80, 175, 252, 539, 704, 891, 1100, 1573, 1872, 2873, 3332, 3825, 4352, 5491, 6156, 8303, 9200, 10143, 11132, 15341, 16704, 18125, 19604, 21141, 22736, 26071, 27900, 35557, 37888, 40293, 42772, 45325, 47952, 56129, 59204, 62361, 65600, 72283, 75852, 86903, 90992, 95175, 99452, 117077, 122112, 127253]

sage: [next_prime_power(n) for n in xrange(0, 72)] #ok A000015    Smallest prime power >= n.

[1, 2, 3, 4, 5, 7, 7, 8, 9, 11, 11, 13, 13, 16, 16, 16, 17, 19, 19, 23, 23, 23, 23, 25, 25, 27, 27, 29, 29, 31, 31, 32, 37, 37, 37, 37, 37, 41, 41, 41, 41, 43, 43, 47, 47, 47, 47, 49, 49, 53, 53, 53, 53, 59, 59, 59, 59, 59, 59, 61, 61, 64, 64, 64, 67, 67, 67, 71, 71, 71, 71, 73]

sage: [next_prime_power(n)*n for n in xrange(0, 72)] #nnnnn

[0, 2, 6, 12, 20, 35, 42, 56, 72, 99, 110, 143, 156, 208, 224, 240, 272, 323, 342, 437, 460, 483, 506, 575, 600, 675, 702, 783, 812, 899, 930, 992, 1184, 1221, 1258, 1295, 1332, 1517, 1558, 1599, 1640, 1763, 1806, 2021, 2068, 2115, 2162, 2303, 2352, 2597, 2650, 2703, 2756, 3127, 3186, 3245, 3304, 3363, 3422, 3599, 3660, 3904, 3968, 4032, 4288, 4355, 4422, 4757, 4828, 4899, 4970, 5183]

sage: [next_prime_power(n^2) for n in xrange(0, 72)] #nnnnnnn

[1, 2, 5, 11, 17, 27, 37, 53, 67, 83, 101, 125, 149, 173, 197, 227, 257, 293, 331, 367, 401, 443, 487, 541, 577, 631, 677, 733, 787, 853, 907, 967, 1031, 1091, 1163, 1229, 1297, 1373, 1447, 1523, 1601, 1693, 1777, 1861, 1949, 2027, 2129, 2213, 2309, 2411, 2503, 2609, 2707, 2819, 2917, 3037, 3137, 3251, 3371, 3491, 3607, 3727, 3847, 3989, 4099, 4229, 4357, 4493, 4637, 4783, 4903, 5051]

sage: [next_prime_power(n)-n for n in xrange(0, 72)] #nnn

[1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 2, 1, 3, 2, 1, 3, 2, 1, 4, 3, 2, 1, 2]

sage: [next_prime_power(n)*next_prime(n) for n in xrange(0, 72)] #nnnnnnn

[2, 4, 9, 20, 25, 49, 49, 88, 99, 121, 121, 169, 169, 272, 272, 272, 289, 361, 361, 529, 529, 529, 529, 725, 725, 783, 783, 841, 841, 961, 961, 1184, 1369, 1369, 1369, 1369, 1369, 1681, 1681, 1681, 1681, 1849, 1849, 2209, 2209, 2209, 2209, 2597, 2597, 2809, 2809, 2809, 2809, 3481, 3481, 3481, 3481, 3481, 3481, 3721, 3721, 4288, 4288, 4288, 4489, 4489, 4489, 5041, 5041, 5041, 5041, 5329]

sage: [next_prime_power(n)-next_prime(n) for n in xrange(0, 72)] #nnnn

[-1, 0, 0, -1, 0, 0, 0, -3, -2, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -4, -4, -2, -2, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0]

sage: [next_prime_power(n)+next_prime(n) for n in xrange(0, 72)] #nnnnn

[3, 4, 6, 9, 10, 14, 14, 19, 20, 22, 22, 26, 26, 33, 33, 33, 34, 38, 38, 46, 46, 46, 46, 54, 54, 56, 56, 58, 58, 62, 62, 69, 74, 74, 74, 74, 74, 82, 82, 82, 82, 86, 86, 94, 94, 94, 94, 102, 102, 106, 106, 106, 106, 118, 118, 118, 118, 118, 118, 122, 122, 131, 131, 131, 134, 134, 134, 142, 142, 142, 142, 146]

sage: [crt(0, n, 3, 2) for n in xrange(0, 50)] #

[0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147]

sage: [crt(1, n, 3, 2) for n in xrange(1, 64)] #ok A016777   
 3n+1.

[1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175, 178, 181, 184, 187]

sage: [crt(2, n, 3, 2) for n in xrange(2, 62)] #ok  A016789   3n+2.

[2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179]

sage: [2*crt(2, n, 3, 2) for n in xrange(2, 48)] #nem beküldeni   6n+4.

[4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82, 88, 94, 100, 106, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274]

sage: [crt(0, n, 3, 3) for n in xrange(0, 50)] #nnnnnnnnnnnnn

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/45.py", line 7, in <module> exec compile(ur'[crt(_sage_const_0 , n, _sage_const_3 , _sage_const_3 ) for n in xrange(_sage_const_0 , _sage_const_50 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(1, n, 3, 3) for n in xrange(0, 50)] #nnnnnn

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/46.py", line 7, in <module> exec compile(ur'[crt(_sage_const_1 , n, _sage_const_3 , _sage_const_3 ) for n in xrange(_sage_const_0 , _sage_const_50 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(2, n, 3, 3) for n in xrange(0, 50)] #nnnnnnnnnn

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/47.py", line 7, in <module> exec compile(ur'[crt(_sage_const_2 , n, _sage_const_3 , _sage_const_3 ) for n in xrange(_sage_const_0 , _sage_const_50 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(3, n, 3, 3) for n in xrange(0, 50)] #nnnnnnnnn

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/48.py", line 7, in <module> exec compile(ur'[crt(_sage_const_3 , n, _sage_const_3 , _sage_const_3 ) for n in xrange(_sage_const_0 , _sage_const_50 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(0, n, 3, 4) for n in xrange(0, 50)] #nnnn

[0, -3, -6, -9, -12, -15, -18, -21, -24, -27, -30, -33, -36, -39, -42, -45, -48, -51, -54, -57, -60, -63, -66, -69, -72, -75, -78, -81, -84, -87, -90, -93, -96, -99, -102, -105, -108, -111, -114, -117, -120, -123, -126, -129, -132, -135, -138, -141, -144, -147]

sage: [crt(1, n, 3, 4) for n in xrange(1, 50)] #nnnnnnnn

[1, -2, -5, -8, -11, -14, -17, -20, -23, -26, -29, -32, -35, -38, -41, -44, -47, -50, -53, -56, -59, -62, -65, -68, -71, -74, -77, -80, -83, -86, -89, -92, -95, -98, -101, -104, -107, -110, -113, -116, -119, -122, -125, -128, -131, -134, -137, -140, -143]

sage: [crt(2, n, 3, 4) for n in xrange(1, 60)] #nnnnnnnnnn A112335   Row sums of number triangle A112334.   1, -1, -4, -7, -10, -13, -16, -19, -22,

[5, 2, -1, -4, -7, -10, -13, -16, -19, -22, -25, -28, -31, -34, -37, -40, -43, -46, -49, -52, -55, -58, -61, -64, -67, -70, -73, -76, -79, -82, -85, -88, -91, -94, -97, -100, -103, -106, -109, -112, -115, -118, -121, -124, -127, -130, -133, -136, -139, -142, -145, -148, -151, -154, -157, -160, -163, -166, -169]

sage: [n+crt(2, n, 3, 4) for n in xrange(4, 60)] #nnnnnnnnA005843    The even numbers: a(n) = 2n.   0, 2, 4, 6, 8, 10, 12, 14, 16,

[0, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20, -22, -24, -26, -28, -30, -32, -34, -36, -38, -40, -42, -44, -46, -48, -50, -52, -54, -56, -58, -60, -62, -64, -66, -68, -70, -72, -74, -76, -78, -80, -82, -84, -86, -88, -90, -92, -94, -96, -98, -100, -102, -104, -106, -108, -110]

sage: [n-crt(2, n, 3, 4) for n in xrange(2, 49)] # ok A008586   Multiples of 4.

[0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184]

sage: [n-crt(2, 2*n, 3, 4) for n in xrange(2, 48)] #ok A017053    (7n+6).

[6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 76, 83, 90, 97, 104, 111, 118, 125, 132, 139, 146, 153, 160, 167, 174, 181, 188, 195, 202, 209, 216, 223, 230, 237, 244, 251, 258, 265, 272, 279, 286, 293, 300, 307, 314, 321]

sage: [n+crt(2, 2*n, 3, 4) for n in xrange(2, 48)] #nnnnnnn

[-2, -7, -12, -17, -22, -27, -32, -37, -42, -47, -52, -57, -62, -67, -72, -77, -82, -87, -92, -97, -102, -107, -112, -117, -122, -127, -132, -137, -142, -147, -152, -157, -162, -167, -172, -177, -182, -187, -192, -197, -202, -207, -212, -217, -222, -227]

sage: [crt(2, -2*n, 3, 4) for n in xrange(-1, 48)] #nem kellA016933  	 	 6n+2.

[2, 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 86, 92, 98, 104, 110, 116, 122, 128, 134, 140, 146, 152, 158, 164, 170, 176, 182, 188, 194, 200, 206, 212, 218, 224, 230, 236, 242, 248, 254, 260, 266, 272, 278, 284, 290]

sage: [crt(2, -(n^2), 3, 4) for n in xrange(0, 48)] #nnnnn

[8, 11, 20, 35, 56, 83, 116, 155, 200, 251, 308, 371, 440, 515, 596, 683, 776, 875, 980, 1091, 1208, 1331, 1460, 1595, 1736, 1883, 2036, 2195, 2360, 2531, 2708, 2891, 3080, 3275, 3476, 3683, 3896, 4115, 4340, 4571, 4808, 5051, 5300, 5555, 5816, 6083, 6356, 6635]

sage: [crt(1, -(n^2), 3, 4) for n in xrange(0, 48)] #nnnnnnnnn

[4, 7, 16, 31, 52, 79, 112, 151, 196, 247, 304, 367, 436, 511, 592, 679, 772, 871, 976, 1087, 1204, 1327, 1456, 1591, 1732, 1879, 2032, 2191, 2356, 2527, 2704, 2887, 3076, 3271, 3472, 3679, 3892, 4111, 4336, 4567, 4804, 5047, 5296, 5551, 5812, 6079, 6352, 6631]

sage: [crt(2, -(n^2), 4, 5) for n in xrange(0, 48)] #nnnnnnnnnn

[10, 14, 26, 46, 74, 110, 154, 206, 266, 334, 410, 494, 586, 686, 794, 910, 1034, 1166, 1306, 1454, 1610, 1774, 1946, 2126, 2314, 2510, 2714, 2926, 3146, 3374, 3610, 3854, 4106, 4366, 4634, 4910, 5194, 5486, 5786, 6094, 6410, 6734, 7066, 7406, 7754, 8110, 8474, 8846]

sage: [crt(2,-(n^2), 4, 5)-crt(1,-(n^2), 3, 4) for n in xrange(0, 50)] #ok A114949  	 	 n^2 + 6.

[6, 7, 10, 15, 22, 31, 42, 55, 70, 87, 106, 127, 150, 175, 202, 231, 262, 295, 330, 367, 406, 447, 490, 535, 582, 631, 682, 735, 790, 847, 906, 967, 1030, 1095, 1162, 1231, 1302, 1375, 1450, 1527, 1606, 1687, 1770, 1855, 1942, 2031, 2122, 2215, 2310, 2407]

sage: [crt(2,-(n^1), 4, 5)*crt(1,-(n^1), 3, 4) for n in xrange(0, 50)] #nnnnnnn

[40, 98, 180, 286, 416, 570, 748, 950, 1176, 1426, 1700, 1998, 2320, 2666, 3036, 3430, 3848, 4290, 4756, 5246, 5760, 6298, 6860, 7446, 8056, 8690, 9348, 10030, 10736, 11466, 12220, 12998, 13800, 14626, 15476, 16350, 17248, 18170, 19116, 20086, 21080, 22098, 23140, 24206, 25296, 26410, 27548, 28710, 29896, 31106]

sage: [crt(2,-(n^(-1)), 4, 5)*crt(1,-(n^(-1)), 3, 4) for n in xrange(1, 50)] #nnnnnnnn

[98.0, 66.0, 56.666666666666671, 52.25, 49.68, 48.0, 46.816326530612244, 45.9375, 45.259259259259267, 44.720000000000006, 44.280991735537185, 43.916666666666671, 43.609467455621306, 43.34693877551021, 43.120000000000005, 42.921875, 42.747404844290656, 42.592592592592595, 42.45429362880887, 42.329999999999998, 42.217687074829932, 42.115702479338843, 42.022684310018903, 41.9375, 41.859200000000001, 41.786982248520715, 41.720164609053498, 41.658163265306122, 41.600475624256838, 41.546666666666667, 41.496357960457857, 41.44921875, 41.404958677685947, 41.363321799307954, 41.324081632653055, 41.287037037037031, 41.252008765522277, 41.218836565096957, 41.187376725838263, 41.157499999999992, 41.129089827483639, 41.102040816326529, 41.076257436452138, 41.051652892561989, 41.028148148148148, 41.005671077504729, 40.984155726573114, 40.963541666666671, 40.943773427738442]

sage: [crt(2,-(n^2), 4, 5)*crt(1,-(n^2), 3, 4) for n in xrange(0, 50)] #nnnnn

[40, 98, 416, 1426, 3848, 8690, 17248, 31106, 52136, 82498, 124640, 181298, 255496, 350546, 470048, 617890, 798248, 1015586, 1274656, 1580498, 1938440, 2354098, 2833376, 3382466, 4007848, 4716290, 5514848, 6410866, 7411976, 8526098, 9761440, 11126498, 12630056, 14281186, 16089248, 18063890, 20215048, 22552946, 25088096, 27831298, 30793640, 33986498, 37421536, 41110706, 45066248, 49300690, 53826848, 58657826, 63807016, 69288098]

sage: [crt(2,-(n^1), 4, 5)-crt(1,-(n^1), 3, 4) for n in xrange(0, 50)] #

[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55]

sage: [crt(2,-(n^3), 4, 5)-crt(1,-(n^3), 3, 4) for n in xrange(0, 50)] #nnnnnnnn

[6, 7, 14, 33, 70, 131, 222, 349, 518, 735, 1006, 1337, 1734, 2203, 2750, 3381, 4102, 4919, 5838, 6865, 8006, 9267, 10654, 12173, 13830, 15631, 17582, 19689, 21958, 24395, 27006, 29797, 32774, 35943, 39310, 42881, 46662, 50659, 54878, 59325, 64006, 68927, 74094, 79513, 85190, 91131, 97342, 103829, 110598, 117655]

sage: [crt(2,-(n^3), 4, 5)*crt(1,-(n^3), 3, 4) for n in xrange(0, 50)] #nnnnnn

[40, 98, 1176, 10030, 52136, 193290, 569848, 1427606, 3169320, 6410866, 12046040, 21319998, 35911336, 58022810, 90480696, 136842790, 201515048, 289876866, 408415000, 564866126, 768368040, 1029619498, 1361048696, 1776990390, 2293871656, 2930406290, 3707797848, 4649951326, 5783693480, 7139001786, 8749242040, 10651414598, 12886409256, 15499268770, 18539461016, 22061159790, 26123534248, 30791046986, 36133760760, 42227653846, 49154944040, 57004421298, 65871789016, 75860013950, 87079684776, 99649379290, 113696040248, 129355359846, 146772172840, 166100858306]

sage: [crt(2,-(n^2), 4, 5)*crt(1,-(n^2), 3, 4)/2 for n in xrange(0, 50)] #nnnnnnnnnn

[20, 49, 208, 713, 1924, 4345, 8624, 15553, 26068, 41249, 62320, 90649, 127748, 175273, 235024, 308945, 399124, 507793, 637328, 790249, 969220, 1177049, 1416688, 1691233, 2003924, 2358145, 2757424, 3205433, 3705988, 4263049, 4880720, 5563249, 6315028, 7140593, 8044624, 9031945, 10107524, 11276473, 12544048, 13915649, 15396820, 16993249, 18710768, 20555353, 22533124, 24650345, 26913424, 29328913, 31903508, 34644049]

sage: [crt(2,-(n^2), 4, 5)/crt(1,-(n^2), 3, 4)*2^n for n in xrange(0, 50)] #nnnnnnnnn

[5/2, 4, 13/2, 368/31, 296/13, 3520/79, 88, 26368/151, 2432/7, 171008/247, 26240/19, 1011712/367, 600064/109, 802816/73, 813056/37, 4259840/97, 16941056/193, 152829952/871, 21397504/61, 762314752/1087, 60293120/43, 3720347648/1327, 72876032/13, 17834180608/1591, 9705619456/433, 84221624320/1879, 11383341056/127, 56103010304/313, 211124486144/589, 258771779584/361, 242262999040/169, 8276401979392/2887, 4408783929344/769, 37503654428672/3271, 710817087488/31, 168706315386880/3679, 12747462934528/139, 753990098747392/4111, 99402723098624/271, 3350211929833472/4567, 1761967383511040/1201, 2115460371841024/721, 1942287290466304/331, 9306266417496064/793, 34102452647100416/1453, 285345257640427520/6079, 37269046135095296/397, 1244963821991231488/6631, 92746004826161152/247, 5412200852192493568/7207]

sage: [crt(2, -(n^2), 4, 5)/2 for n in xrange(0, 48)] #nnnnnnnn

[5, 7, 13, 23, 37, 55, 77, 103, 133, 167, 205, 247, 293, 343, 397, 455, 517, 583, 653, 727, 805, 887, 973, 1063, 1157, 1255, 1357, 1463, 1573, 1687, 1805, 1927, 2053, 2183, 2317, 2455, 2597, 2743, 2893, 3047, 3205, 3367, 3533, 3703, 3877, 4055, 4237, 4423]

sage: [crt(2, -(n^3), 4, 5) for n in xrange(0, 48)] #nnnnnnnnnnnnn

[10, 14, 42, 118, 266, 510, 874, 1382, 2058, 2926, 4010, 5334, 6922, 8798, 10986, 13510, 16394, 19662, 23338, 27446, 32010, 37054, 42602, 48678, 55306, 62510, 70314, 78742, 87818, 97566, 108010, 119174, 131082, 143758, 157226, 171510, 186634, 202622, 219498, 237286, 256010, 275694, 296362, 318038, 340746, 364510, 389354, 415302]

sage: [crt(2, -(n^3), 4, 5)/2 for n in xrange(0, 48)] #nnnnnnn

[5, 7, 21, 59, 133, 255, 437, 691, 1029, 1463, 2005, 2667, 3461, 4399, 5493, 6755, 8197, 9831, 11669, 13723, 16005, 18527, 21301, 24339, 27653, 31255, 35157, 39371, 43909, 48783, 54005, 59587, 65541, 71879, 78613, 85755, 93317, 101311, 109749, 118643, 128005, 137847, 148181, 159019, 170373, 182255, 194677, 207651]

sage: [crt(2, -(n^3), 4, 5)-crt(1, -(n^3), 4, 5)  for n in xrange(0, 48)] #

[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]

sage: [crt(2, -(n^3), 4, 5)-crt(1, -(n^2), 4, 5)  for n in xrange(0, 48)] #nnnnnnnn

[5, 5, 21, 77, 197, 405, 725, 1181, 1797, 2597, 3605, 4845, 6341, 8117, 10197, 12605, 15365, 18501, 22037, 25997, 30405, 35285, 40661, 46557, 52997, 60005, 67605, 75821, 84677, 94197, 104405, 115325, 126981, 139397, 152597, 166605, 181445, 197141, 213717, 231197, 249605, 268965, 289301, 310637, 332997, 356405, 380885, 406461]

sage: [crt(1, -(n^3), 4, 5) for n in xrange(0, 48)] #nnnnnnnnnn

[5, 9, 37, 113, 261, 505, 869, 1377, 2053, 2921, 4005, 5329, 6917, 8793, 10981, 13505, 16389, 19657, 23333, 27441, 32005, 37049, 42597, 48673, 55301, 62505, 70309, 78737, 87813, 97561, 108005, 119169, 131077, 143753, 157221, 171505, 186629, 202617, 219493, 237281, 256005, 275689, 296357, 318033, 340741, 364505, 389349, 415297]

sage: [crt(1, -(n^3), 2, 5) for n in xrange(0, 48)] #

[5, 9, 37, 113, 261, 505, 869, 1377, 2053, 2921, 4005, 5329, 6917, 8793, 10981, 13505, 16389, 19657, 23333, 27441, 32005, 37049, 42597, 48673, 55301, 62505, 70309, 78737, 87813, 97561, 108005, 119169, 131077, 143753, 157221, 171505, 186629, 202617, 219493, 237281, 256005, 275689, 296357, 318033, 340741, 364505, 389349, 415297]

sage: [crt(1, -(n^3), 3, 5) for n in xrange(0, 48)] #nnnnnnnnnn

[-5, -11, -53, -167, -389, -755, -1301, -2063, -3077, -4379, -6005, -7991, -10373, -13187, -16469, -20255, -24581, -29483, -34997, -41159, -48005, -55571, -63893, -73007, -82949, -93755, -105461, -118103, -131717, -146339, -162005, -178751, -196613, -215627, -235829, -257255, -279941, -303923, -329237, -355919, -384005, -413531, -444533, -477047, -511109, -546755, -584021, -622943]

sage: [n-2*(crt(2, n, 3, 4)) for n in xrange(3, 49)] #beküldeni?A017041  (7n+5).

[5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75, 82, 89, 96, 103, 110, 117, 124, 131, 138, 145, 152, 159, 166, 173, 180, 187, 194, 201, 208, 215, 222, 229, 236, 243, 250, 257, 264, 271, 278, 285, 292, 299, 306, 313, 320]

sage: [crt(3, n, 3, 4) for n in xrange(4, 60)] #nnnn sage: [crt(0, n, 3, 4) for n in xrange(0, 50)] #nnnn

[0, -3, -6, -9, -12, -15, -18, -21, -24, -27, -30, -33, -36, -39, -42, -45, -48, -51, -54, -57, -60, -63, -66, -69, -72, -75, -78, -81, -84, -87, -90, -93, -96, -99, -102, -105, -108, -111, -114, -117, -120, -123, -126, -129, -132, -135, -138, -141, -144, -147, -150, -153, -156, -159, -162, -165]

sage: [n+crt(4, n, 3, 4) for n in xrange(4, 60)] #

[8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20, -22, -24, -26, -28, -30, -32, -34, -36, -38, -40, -42, -44, -46, -48, -50, -52, -54, -56, -58, -60, -62, -64, -66, -68, -70, -72, -74, -76, -78, -80, -82, -84, -86, -88, -90, -92, -94, -96, -98, -100, -102]

sage: [crt(0, n, 3, 5) for n in xrange(0, 59)] #ok A008588 alatta    Multiples of 6.

[0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348, 354]

sage: [crt(6, n, 3, 5) for n in xrange(5, 65)] #ok A008588 felette     Multiples of 6.

[0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348, 354]

sage: [crt(1, n, 3, 5) for n in xrange(1, 57)] #beküldeni? A016921  6n+1.

[1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 187, 193, 199, 205, 211, 217, 223, 229, 235, 241, 247, 253, 259, 265, 271, 277, 283, 289, 295, 301, 307, 313, 319, 325, 331]

sage: [crt(2, n, 3, 5)/2 for n in xrange(2, 57)] #nem kell A016777  	 	 3n+1.

[1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163]

sage: [crt(2, n, 3, 5)^2 for n in xrange(2, 34)] #ok A016934  	 	 (6n+2)^2.

[4, 64, 196, 400, 676, 1024, 1444, 1936, 2500, 3136, 3844, 4624, 5476, 6400, 7396, 8464, 9604, 10816, 12100, 13456, 14884, 16384, 17956, 19600, 21316, 23104, 24964, 26896, 28900, 30976, 33124, 35344]

sage: [crt(2, n, 3, 5)^3 for n in xrange(2, 27)] #ok A016935  	 	 (6n+2)^3.

[8, 512, 2744, 8000, 17576, 32768, 54872, 85184, 125000, 175616, 238328, 314432, 405224, 512000, 636056, 778688, 941192, 1124864, 1331000, 1560896, 1815848, 2097152, 2406104, 2744000, 3112136]

sage: [crt(2, n, 3, 5)^3/8 for n in xrange(2, 31)] #ok A016779    (3n+1)^3.

[1, 64, 343, 1000, 2197, 4096, 6859, 10648, 15625, 21952, 29791, 39304, 50653, 64000, 79507, 97336, 117649, 140608, 166375, 195112, 226981, 262144, 300763, 343000, 389017, 438976, 493039, 551368, 614125]

sage: [crt(2, n, 3, 5)^3/8^(n-1) for n in xrange(2, 31)] #nnnnnnnnn

[1, 8, 343/64, 125/64, 2197/4096, 1/8, 6859/262144, 1331/262144, 15625/16777216, 343/2097152, 29791/1073741824, 4913/1073741824, 50653/68719476736, 125/1073741824, 79507/4398046511104, 12167/4398046511104, 117649/281474976710656, 2197/35184372088832, 166375/18014398509481984, 24389/18014398509481984, 226981/1152921504606846976, 1/35184372088832, 300763/73786976294838206464, 42875/73786976294838206464, 389017/4722366482869645213696, 6859/590295810358705651712, 493039/302231454903657293676544, 68921/302231454903657293676544, 614125/19342813113834066795298816]

sage: [crt(2, n, 3, 5)^4 for n in xrange(2, 24)] # ok A016936  	 	 (6n+2)^4.

[16, 4096, 38416, 160000, 456976, 1048576, 2085136, 3748096, 6250000, 9834496, 14776336, 21381376, 29986576, 40960000, 54700816, 71639296, 92236816, 116985856, 146410000, 181063936, 221533456, 268435456]

sage: [crt(2, n, 3, 5)^4/16 for n in xrange(2, 26)] # ok A016780    (3n+1)^4.

[1, 256, 2401, 10000, 28561, 65536, 130321, 234256, 390625, 614656, 923521, 1336336, 1874161, 2560000, 3418801, 4477456, 5764801, 7311616, 9150625, 11316496, 13845841, 16777216, 20151121, 24010000]

sage: [crt(2, n, 3, 5)^2/2 for n in xrange(2, 34)] #nnnnnnnn

[2, 32, 98, 200, 338, 512, 722, 968, 1250, 1568, 1922, 2312, 2738, 3200, 3698, 4232, 4802, 5408, 6050, 6728, 7442, 8192, 8978, 9800, 10658, 11552, 12482, 13448, 14450, 15488, 16562, 17672]

sage: [crt(2, n, 3, 5)^2/4 for n in xrange(2, 38)] #ok A016778    (3n+1)^2.

[1, 16, 49, 100, 169, 256, 361, 484, 625, 784, 961, 1156, 1369, 1600, 1849, 2116, 2401, 2704, 3025, 3364, 3721, 4096, 4489, 4900, 5329, 5776, 6241, 6724, 7225, 7744, 8281, 8836, 9409, 10000, 10609, 11236]

sage: [crt(2, n, 3, 5)^5 for n in xrange(2, 21)] #ok A016937  (6n+2)^5.

[32, 32768, 537824, 3200000, 11881376, 33554432, 79235168, 164916224, 312500000, 550731776, 916132832, 1453933568, 2219006624, 3276800000, 4704270176, 6590815232, 9039207968, 12166529024, 16105100000]

sage: [crt(2, n, 3, 5)^5/32 for n in xrange(2, 23)] #ok A016781   (3n+1)^5.

[1, 1024, 16807, 100000, 371293, 1048576, 2476099, 5153632, 9765625, 17210368, 28629151, 45435424, 69343957, 102400000, 147008443, 205962976, 282475249, 380204032, 503284375, 656356768, 844596301]

sage: [crt(2, n, 3, 5)^6 for n in xrange(2, 19)] #A016938   	 	 (6n+2)^6.

[64, 262144, 7529536, 64000000, 308915776, 1073741824, 3010936384, 7256313856, 15625000000, 30840979456, 56800235584, 98867482624, 164206490176, 262144000000, 404567235136, 606355001344, 885842380864]

sage: [crt(2, n, 3, 5)^6/2^6 for n in xrange(2, 21)] #ok A016782   (3n+1)^6.

[1, 4096, 117649, 1000000, 4826809, 16777216, 47045881, 113379904, 244140625, 481890304, 887503681, 1544804416, 2565726409, 4096000000, 6321363049, 9474296896, 13841287201, 19770609664, 27680640625]

sage: [crt(2, n, 3, 5)^7 for n in xrange(2, 17)] #ok A016939  	 	 (6n+2)^7.

[128, 2097152, 105413504, 1280000000, 8031810176, 34359738368, 114415582592, 319277809664, 781250000000, 1727094849536, 3521614606208, 6722988818432, 12151280273024, 20971520000000, 34792782221696]

sage: [crt(2, n, 3, 5)^7/2^7 for n in xrange(2, 20)] #ok A016783    (3n+1)^7.

[1, 16384, 823543, 10000000, 62748517, 268435456, 893871739, 2494357888, 6103515625, 13492928512, 27512614111, 52523350144, 94931877133, 163840000000, 271818611107, 435817657216, 678223072849, 1028071702528]

sage: [crt(2, n, 3, 5)^8 for n in xrange(2, 16)] # ok A016940  	 	 (6n+2)^8.

[256, 16777216, 1475789056, 25600000000, 208827064576, 1099511627776, 4347792138496, 14048223625216, 39062500000000, 96717311574016, 218340105584896, 457163239653376, 899194740203776, 1677721600000000]

sage: [crt(2, n, 3, 5)^8/2^8 for n in xrange(2, 18)] # ok A016784  (3n+1)^8.  )] #

[1, 65536, 5764801, 100000000, 815730721, 4294967296, 16983563041, 54875873536, 152587890625, 377801998336, 852891037441, 1785793904896, 3512479453921, 6553600000000, 11688200277601, 20047612231936]

sage: [crt(2, n, 3, 5)^9 for n in xrange(2, 15)] #ok A016941  	 	 (6n+2)^9.

[512, 134217728, 20661046784, 512000000000, 5429503678976, 35184372088832, 165216101262848, 618121839509504, 1953125000000000, 5416169448144896, 13537086546263552, 31087100296429568, 66540410775079424]

sage: [crt(2, n, 3, 5)^9/2^9 for n in xrange(2, 17)] #ok A016785   (3n+1)^9.

[1, 262144, 40353607, 1000000000, 10604499373, 68719476736, 322687697779, 1207269217792, 3814697265625, 10578455953408, 26439622160671, 60716992766464, 129961739795077, 262144000000000, 502592611936843]

sage: [crt(2, n, 3, 5)^10 for n in xrange(2, 14)] #ok A016942  	 	 (6n+2)^10.

[1024, 1073741824, 289254654976, 10240000000000, 141167095653376, 1125899906842624, 6278211847988224, 27197360938418176, 97656250000000000, 303305489096114176, 839299365868340224, 2113922820157210624]

sage: [crt(2, n, 3, 5)^10/2^10 for n in xrange(2, 16)] #ok A016786    (3n+1)^10.

[1, 1048576, 282475249, 10000000000, 137858491849, 1099511627776, 6131066257801, 26559922791424, 95367431640625, 296196766695424, 819628286980801, 2064377754059776, 4808584372417849, 10485760000000000]

sage: [crt(2, n, 3, 5)^11 for n in xrange(2, 13)] #ok A016943  	 	 (6n+2)^11.

[2048, 8589934592, 4049565169664, 204800000000000, 3670344486987776, 36028797018963968, 238572050223552512, 1196683881290399744, 4882812500000000000, 16985107389382393856, 52036560683837093888]

sage: [crt(2, n, 3, 5)^11/2^11 for n in xrange(2, 15)] #A016787    (3n+1)^11.

[1, 4194304, 1977326743, 100000000000, 1792160394037, 17592186044416, 116490258898219, 584318301411328, 2384185791015625, 8293509467471872, 25408476896404831, 70188843638032384, 177917621779460413]

sage: [crt(2, n, 3, 5)^12 for n in xrange(2, 13)] #folytatni??????

sage: [crt(2, n, 3, 5)^12/2^12 for n in xrange(2, 15)] #folytatni??????

sage: [crt(3, n, 3, 5) for n in xrange(3, 50)] #ok A016945  	 	 6n+3.

[3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, 105, 111, 117, 123, 129, 135, 141, 147, 153, 159, 165, 171, 177, 183, 189, 195, 201, 207, 213, 219, 225, 231, 237, 243, 249, 255, 261, 267, 273, 279]

sage: [crt(4, n, 3, 5)+crt(3, n, 3, 5) for n in xrange(3, 50)]#okA017533 (12n+1).

[1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 133, 145, 157, 169, 181, 193, 205, 217, 229, 241, 253, 265, 277, 289, 301, 313, 325, 337, 349, 361, 373, 385, 397, 409, 421, 433, 445, 457, 469, 481, 493, 505, 517, 529, 541, 553]

sage: [crt(4, n, 3, 5)*crt(3, n, 3, 5)/6 for n in xrange(4, 50)] #nnnnnnn

[6, 25, 56, 99, 154, 221, 300, 391, 494, 609, 736, 875, 1026, 1189, 1364, 1551, 1750, 1961, 2184, 2419, 2666, 2925, 3196, 3479, 3774, 4081, 4400, 4731, 5074, 5429, 5796, 6175, 6566, 6969, 7384, 7811, 8250, 8701, 9164, 9639, 10126, 10625, 11136, 11659, 12194, 12741]

sage: [crt(4, n, 3, 5) for n in xrange(4, 50)] #ok A016957  6n+4.

[4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82, 88, 94, 100, 106, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274]

sage: [crt(4, n, 3, 5)^2 for n in xrange(4, 35)] # ok A016958  	 	 (6n+4)^2. ezt is (A016790 n)^2 és így tovább

[16, 100, 256, 484, 784, 1156, 1600, 2116, 2704, 3364, 4096, 4900, 5776, 6724, 7744, 8836, 10000, 11236, 12544, 13924, 15376, 16900, 18496, 20164, 21904, 23716, 25600, 27556, 29584, 31684, 33856]

sage: [crt(4, n, 3, 5)^2/4 for n in xrange(4, 40)] #ok A016790  	 	 (3n+2)^2.

[4, 25, 64, 121, 196, 289, 400, 529, 676, 841, 1024, 1225, 1444, 1681, 1936, 2209, 2500, 2809, 3136, 3481, 3844, 4225, 4624, 5041, 5476, 5929, 6400, 6889, 7396, 7921, 8464, 9025, 9604, 10201, 10816, 11449]

sage: [crt(4, n, 3, 5)^2/2^2 for n in xrange(4, 40)] #beküldeni, folytatni A016790  	 	 (3n+2)^2. ezt is A016958/2^2 és így tovább

[4, 25, 64, 121, 196, 289, 400, 529, 676, 841, 1024, 1225, 1444, 1681, 1936, 2209, 2500, 2809, 3136, 3481, 3844, 4225, 4624, 5041, 5476, 5929, 6400, 6889, 7396, 7921, 8464, 9025, 9604, 10201, 10816, 11449]

sage: [crt(5, n, 3, 5) for n in xrange(5, 61)] #A016969  	 	 6n+5. beküldeni? A016969  	 	 6n+5.

[5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197, 203, 209, 215, 221, 227, 233, 239, 245, 251, 257, 263, 269, 275, 281, 287, 293, 299, 305, 311, 317, 323, 329, 335]

sage: [crt(5, n, 3, 5)^2 for n in xrange(4, 61)] #nnnnnnnnnnnnnnn

[1, 25, 121, 289, 529, 841, 1225, 1681, 2209, 2809, 3481, 4225, 5041, 5929, 6889, 7921, 9025, 10201, 11449, 12769, 14161, 15625, 17161, 18769, 20449, 22201, 24025, 25921, 27889, 29929, 32041, 34225, 36481, 38809, 41209, 43681, 46225, 48841, 51529, 54289, 57121, 60025, 63001, 66049, 69169, 72361, 75625, 78961, 82369, 85849, 89401, 93025, 96721, 100489, 104329, 108241, 112225]

sage: [crt(6, n, 3, 5)^2/6 for n in xrange(5, 50)] #ok A033581    6n^2.

[0, 6, 24, 54, 96, 150, 216, 294, 384, 486, 600, 726, 864, 1014, 1176, 1350, 1536, 1734, 1944, 2166, 2400, 2646, 2904, 3174, 3456, 3750, 4056, 4374, 4704, 5046, 5400, 5766, 6144, 6534, 6936, 7350, 7776, 8214, 8664, 9126, 9600, 10086, 10584, 11094, 11616]

sage: [crt(6, n, 3, 6) for n in xrange(7, 57)] #1-6 mind ilyen

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/97.py", line 7, in <module> exec compile(ur'[crt(_sage_const_6 , n, _sage_const_3 , _sage_const_6 ) for n in xrange(_sage_const_7 , _sage_const_57 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(0, n, 3, 5) for n in xrange(0, 59)] #ugyanaz mint a végén kettő  (beküldeni) A008588    Multiples of 6.

[0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348]

sage: [crt(1, n, 3, 7) for n in xrange(1, 57)] #

[1, -5, -11, -17, -23, -29, -35, -41, -47, -53, -59, -65, -71, -77, -83, -89, -95, -101, -107, -113, -119, -125, -131, -137, -143, -149, -155, -161, -167, -173, -179, -185, -191, -197, -203, -209, -215, -221, -227, -233, -239, -245, -251, -257, -263, -269, -275, -281, -287, -293, -299, -305, -311, -317, -323, -329]

sage: [crt(2, n, 3, 7) for n in xrange(2, 49)] #    6n+2.

[2, -4, -10, -16, -22, -28, -34, -40, -46, -52, -58, -64, -70, -76, -82, -88, -94, -100, -106, -112, -118, -124, -130, -136, -142, -148, -154, -160, -166, -172, -178, -184, -190, -196, -202, -208, -214, -220, -226, -232, -238, -244, -250, -256, -262, -268, -274]

sage: [crt(3, n, 3, 7) for n in xrange(3, 50)] #

[3, -3, -9, -15, -21, -27, -33, -39, -45, -51, -57, -63, -69, -75, -81, -87, -93, -99, -105, -111, -117, -123, -129, -135, -141, -147, -153, -159, -165, -171, -177, -183, -189, -195, -201, -207, -213, -219, -225, -231, -237, -243, -249, -255, -261, -267, -273]

sage: [crt(4, n, 3, 7) for n in xrange(4, 50)] #

[4, -2, -8, -14, -20, -26, -32, -38, -44, -50, -56, -62, -68, -74, -80, -86, -92, -98, -104, -110, -116, -122, -128, -134, -140, -146, -152, -158, -164, -170, -176, -182, -188, -194, -200, -206, -212, -218, -224, -230, -236, -242, -248, -254, -260, -266]

sage: [crt(5, n, 3, 7) for n in xrange(5, 61)] #nem beküldeni A016969    6n+5.

[5, -1, -7, -13, -19, -25, -31, -37, -43, -49, -55, -61, -67, -73, -79, -85, -91, -97, -103, -109, -115, -121, -127, -133, -139, -145, -151, -157, -163, -169, -175, -181, -187, -193, -199, -205, -211, -217, -223, -229, -235, -241, -247, -253, -259, -265, -271, -277, -283, -289, -295, -301, -307, -313, -319, -325]

sage: [crt(6, n, 3, 7) for n in xrange(5, 50)] #

[12, 6, 0, -6, -12, -18, -24, -30, -36, -42, -48, -54, -60, -66, -72, -78, -84, -90, -96, -102, -108, -114, -120, -126, -132, -138, -144, -150, -156, -162, -168, -174, -180, -186, -192, -198, -204, -210, -216, -222, -228, -234, -240, -246, -252]

sage: [crt(0, n, 4,1 ) for n in xrange(0, 59)] #ugyanaz mint felette beküldeni A008588    Multiples of 6.

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

sage: [crt(0, n, 4,2 ) for n in xrange(0, 50)] #

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/106.py", line 7, in <module> exec compile(ur'[crt(_sage_const_0 , n, _sage_const_4 ,_sage_const_2 ) for n in xrange(_sage_const_0 , _sage_const_50 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(0,n,4,3 ) for n in xrange(0, 47)] #nem beküldeni A008586  Multiples of 4.

[0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184]

sage: [crt(0,n,4,3 )*crt(1, n, 4,3 )/4 for n in xrange(0, 47)]#okA001107 10-gonal (or decagonal) numbers: 4n^2 - 3n.

[0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326]

sage: [crt(1, n, 4,3 ) for n in xrange(1, 49)] #ok A016813  4n+1.

[1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189]

sage: [crt(2,n,4,3 )*crt(1,n,4,3 )/2 for n in xrange(2, 54)]# nnnnnnnnn

[5, 27, 65, 119, 189, 275, 377, 495, 629, 779, 945, 1127, 1325, 1539, 1769, 2015, 2277, 2555, 2849, 3159, 3485, 3827, 4185, 4559, 4949, 5355, 5777, 6215, 6669, 7139, 7625, 8127, 8645, 9179, 9729, 10295, 10877, 11475, 12089, 12719, 13365, 14027, 14705, 15399, 16109, 16835, 17577, 18335, 19109, 19899, 20705, 21527]

sage: [crt(2,n,4,3 )+crt(1,n,4,3 ) for n in xrange(2, 54)]# ok A004771 a(n) = 8n+7. Or, numbers n such that binary expansion ends 111.

[7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 119, 127, 135, 143, 151, 159, 167, 175, 183, 191, 199, 207, 215, 223, 231, 239, 247, 255, 263, 271, 279, 287, 295, 303, 311, 319, 327, 335, 343, 351, 359, 367, 375, 383, 391, 399, 407, 415]

sage: [crt(2, n, 4,3 ) for n in xrange(2, 61)] #ok A016825    Numbers congruent to 2 mod 4: a(n) = 4n+2.

[2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 218, 222, 226, 230, 234]

sage: [crt(2, n, 4,3 )/2 for n in xrange(2, 61)] #nem kell

[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117]

sage: [crt(3, n, 4,3 ) for n in xrange(3, 51)] #ok A004767  4n+3.

[3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 191]

sage: [crt(1, n, 4,4 ) for n in xrange(3, 51)] #

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/121.py", line 7, in <module> exec compile(ur'[crt(_sage_const_1 , n, _sage_const_4 ,_sage_const_4 ) for n in xrange(_sage_const_3 , _sage_const_51 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(2, n, 4,4 ) for n in xrange(3, 51)] #

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/122.py", line 7, in <module> exec compile(ur'[crt(_sage_const_2 , n, _sage_const_4 ,_sage_const_4 ) for n in xrange(_sage_const_3 , _sage_const_51 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(5*n, 2*n, 2,5 ) for n in xrange(0, 41)] #beküldeni (júli. 7. )A008599  	 	 Multiples of 17.

[0, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340, 357, 374, 391, 408, 425, 442, 459, 476, 493, 510, 527, 544, 561, 578, 595, 612, 629, 646, 663, 680]

sage: [crt(5*n, 3*n, 2,5 ) for n in xrange(0, 42)] #beküldeni (júli. 7. )A008595  	 	 Multiples of 13.

[0, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390, 403, 416, 429, 442, 455, 468, 481, 494, 507, 520, 533]

sage: [crt(5*n, 4*n, 2,5 ) for n in xrange(0, 43)] #beküldeni (júli. 7. )A008591  	 	 Multiples of 9.

[0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360]

sage: [crt(11*n, n, 1,5 ) for n in xrange(0, 41)] #

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]

sage: [crt(11*n, n, 2,5 ) for n in xrange(0, 41)] #nnnnnnnnnn

[0, 51, 102, 153, 204, 255, 306, 357, 408, 459, 510, 561, 612, 663, 714, 765, 816, 867, 918, 969, 1020, 1071, 1122, 1173, 1224, 1275, 1326, 1377, 1428, 1479, 1530, 1581, 1632, 1683, 1734, 1785, 1836, 1887, 1938, 1989, 2040]

sage: [crt(11*n, 2*n, 2,5 ) for n in xrange(0, 41)] #

[0, 47, 94, 141, 188, 235, 282, 329, 376, 423, 470, 517, 564, 611, 658, 705, 752, 799, 846, 893, 940, 987, 1034, 1081, 1128, 1175, 1222, 1269, 1316, 1363, 1410, 1457, 1504, 1551, 1598, 1645, 1692, 1739, 1786, 1833, 1880]

sage: [crt(11*n, n, 2,5 )-crt(11*n, 2*n, 2,5 )  for n in xrange(0, 41)] #

[0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160]

sage: [crt(11*n, n, 3,5 ) for n in xrange(0, 41)] #

[0, -49, -98, -147, -196, -245, -294, -343, -392, -441, -490, -539, -588, -637, -686, -735, -784, -833, -882, -931, -980, -1029, -1078, -1127, -1176, -1225, -1274, -1323, -1372, -1421, -1470, -1519, -1568, -1617, -1666, -1715, -1764, -1813, -1862, -1911, -1960]

sage: [crt(11*n,2*n,2,3 ) for n in xrange(0, 41)] #n

[0, 29, 58, 87, 116, 145, 174, 203, 232, 261, 290, 319, 348, 377, 406, 435, 464, 493, 522, 551, 580, 609, 638, 667, 696, 725, 754, 783, 812, 841, 870, 899, 928, 957, 986, 1015, 1044, 1073, 1102, 1131, 1160]

sage: [crt(2*n, n, 2,5 ) for n in xrange(0, 51)] #

[0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300]

sage: [crt(2*n, n, 2,6 ) for n in xrange(0, 51)] #

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/128.py", line 7, in <module> exec compile(ur'[crt(_sage_const_2 *n, n, _sage_const_2 ,_sage_const_6 ) for n in xrange(_sage_const_0 , _sage_const_51 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(2*n, n, 2,7 ) for n in xrange(0, 51)] #

[0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400]

sage: [crt(2*n, n, 2,9 ) for n in xrange(0, 51)] #

[0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500]

sage: [crt(2*n, n, 2,11 ) for n in xrange(0, 51)] #

[0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 588, 600]

sage: [crt(2*n, n, 2,13 ) for n in xrange(0, 51)] #

[0, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350, 364, 378, 392, 406, 420, 434, 448, 462, 476, 490, 504, 518, 532, 546, 560, 574, 588, 602, 616, 630, 644, 658, 672, 686, 700]

sage: [crt(2*n, n, 2,15 ) for n in xrange(0, 51)] #

[0, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 400, 416, 432, 448, 464, 480, 496, 512, 528, 544, 560, 576, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 784, 800]

sage: [crt(2*n, n, 1,15 ) for n in xrange(0, 51)] #

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]

sage: [crt(2*n, n, 3,15 ) for n in xrange(0, 51)] #

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/136.py", line 7, in <module> exec compile(ur'[crt(_sage_const_2 *n, n, _sage_const_3 ,_sage_const_15 ) for n in xrange(_sage_const_0 , _sage_const_51 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [-crt(2*n, n, 4,15 ) for n in xrange(0, 42)] #beküldeni A008596    Multiples of 14.

[0, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350, 364, 378, 392, 406, 420, 434, 448, 462, 476, 490, 504, 518, 532, 546, 560, 574]

sage: [crt(2, 2, 2,n ) for n in xrange(0, 51)] #

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/Zlajos/24/code/148.py", line 7, in <module> exec compile(ur'[crt(_sage_const_2 , _sage_const_2 , _sage_const_2 ,n ) for n in xrange(_sage_const_0 , _sage_const_51 )] #' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/sage/rings/arith.py", line 2333, in crt raise ValueError, "arguments a and b must be coprime" ValueError: arguments a and b must be coprime

sage: [crt(n+11, 3, 1,11 ) for n in xrange(0, 51)] #

[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]