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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. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Apr 10 2016

STATUS

approved

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Last modified June 24 16:57 EDT 2021. Contains 345417 sequences. (Running on oeis4.)