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Product formulae

Project: Sophie
Views: 24
Visibility: Unlisted (only visible to those who know the link)
Image: ubuntu2204
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Kernel: SageMath 10.4
l=[3,5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161,74207281,77232917,82589933];
def prodmersenne(k):
    a=1;
    b=1;
    for n in range(0,k):
        if l[n]%4==1:
            a=a*l[n]/(l[n]-1)
        elif l[n]%4==3:
            b=b*l[n]/(l[n]+1)
    return N(lucas_number2(4,4,1)/(lucas_number1(3,3,2)*lucas_number1(5,3,2))*a*b,digits=22)

prodmersenne(50)
0.7853981638978724180271
N(2*pi/2^3,digits=22)
0.7853981633974483096157
l3=[3,7,13,71,103,541,1091,1367,1627,4177,9011,9551,36913,43063,49681,57917,483611,877843,2215303,3598867,7973131,8530117];
def prodrepunitbase3(k):
    a=1;
    b=1;
    for n in range(0,k):
        if l3[n]%4==1:
            a=a*l3[n]/(l3[n]-1)
        elif l3[n]%4==3:
            b=b*l3[n]/(l3[n]+1)
    return N(lucas_number2(4,5,1)/(lucas_number1(3,4,3)*lucas_number1(5,4,3))*a*b,digits=22)

prodrepunitbase3(22)
0.2325363070638513573344
N(2*pi/3^3,digits=22)
0.2327105669325772769232
l7=[5, 13, 131, 149, 1699, 14221, 35201, 126037, 371669, 1264699];
def prodrepunitbase7(k):
    a=1;
    b=1;
    for n in range(0,k):
        if l7[n]%4==1:
            a=a*l7[n]/(l7[n]-1)
        elif l7[n]%4==3:
            b=b*l7[n]/(l7[n]+1)
    return N(lucas_number2(4,7,1)/(lucas_number1(3,8,7)*lucas_number1(5,8,7))*a*b,digits=22)

prodrepunitbase7(10)
0.01869390414817623184134
N(2*pi/7^3,digits=22)
0.01831832451072765736713