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

0,1

Links

Table of n, a(n) for n=0..99.

Steven R. Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math/0604465 [math.NT], 2006-2016.

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.

Example

0.81210571116312251170625096458188717656057710048366992436092182...

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

Crossrefs

Cf. A046073, A105612.

Sequence in context: A198830 A254244 A232068 * A010154 A109011 A225767

Adjacent sequences: A271544 A271545 A271546 * A271548 A271549 A271550

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 10 2016

Status

approved