A271547 Decimal expansion of Product_{p prime} (1+1/(2p))*sqrt(1-1/p), a constant related to the asymptotic average number of squares modulo n.
8, 1, 2, 1, 0, 5, 7, 1, 1, 1, 6, 3, 1, 2, 2, 5, 1, 1, 7, 0, 6, 2, 5, 0, 9, 6, 4, 5, 8, 1, 8, 8, 7, 1, 7, 6, 5, 6, 0, 5, 7, 7, 1, 0, 0, 4, 8, 3, 6, 6, 9, 9, 2, 4, 3, 6, 0, 9, 2, 1, 8, 2, 0, 0, 3, 7, 8, 0, 9, 4, 0, 6, 2, 0, 4, 2, 5, 3, 2, 2, 0, 7, 5, 5, 8, 0, 2, 5, 4, 0, 2, 3, 5, 0, 4, 0, 2, 9, 9, 8
Offset: 0
Examples
0.81210571116312251170625096458188717656057710048366992436092182...
Links
- Steven R. Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math/0604465 [math.NT], 2006-2016.
Programs
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Mathematica
digits = 100; Exp[NSum[-( (-1)^n + 2^(n - 1))*PrimeZetaP[n]/(n* 2^n), {n, 2, Infinity}, NSumTerms -> 3 digits, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First
Formula
Equals exp(Sum_{n>=2} -((-1)^n + 2^(n-1))*P(n)/(n*2^n)), where P(n) is the prime zeta P function.