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A269472 Decimal expansion of Product_{p prime} (1-(p^2+2)/(2(p^2+1)(p+1))) / sqrt(1-1/p), a constant related to the asymptotic average number of squares modulo n. 0
1, 2, 5, 6, 9, 1, 3, 6, 1, 0, 2, 1, 0, 1, 8, 8, 5, 9, 5, 9, 4, 9, 2, 1, 1, 5, 7, 6, 9, 4, 6, 8, 6, 0, 8, 9, 4, 9, 4, 0, 4, 5, 9, 8, 8, 6, 8, 0, 7, 5, 0, 8, 7, 6, 7, 7, 9, 8, 5, 7, 1, 8, 1, 9, 3, 4, 7, 5, 1, 8, 2, 3, 8, 4, 5, 7, 4, 5, 4, 1, 4, 8, 7, 5, 5, 3, 9, 7, 5, 4, 8, 9, 7, 8, 6, 4, 9, 1, 1, 5, 7, 6, 4, 5, 0, 9, 9, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..108.

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

EXAMPLE

1.2569136102101885959492115769468608949404598868075...

MATHEMATICA

digits = 104; m0 = 100; Clear[s]; s[m_] := s[m] = Sum[(1 + 2*(-1)^n - 4*(-1)^n*ChebyshevT[n, 1/4] + 4*Switch[Mod[n, 4], 2, -1, 3, 0, 0, 1, 1, 0])/(2*n) PrimeZetaP[n], {n, 2, m}] // N[#, digits]& // Exp; s[m0]; s[m = 2 m0]; While[RealDigits[s[m], 10, digits] != RealDigits[s[m/2], 10, digits], m = 2 m; Print[m]]; RealDigits[s[m]][[1]]

$MaxExtraPrecision = 1000; Clear[f]; f[p_] := (1 - (p^2 + 2)/(2 (p^2 + 1) (p + 1)))/ Sqrt[1 - 1/p]; Do[c = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x]]; Print[f[2] * Exp[N[Sum[Indexed[c, n]*(PrimeZetaP[n] - 1/2^n), {n, 2, m}], 112]]], {m, 100, 1000, 100}] (* Vaclav Kotesovec, Jun 19 2020 *)

CROSSREFS

Cf. A046073, A105612, A271547.

Sequence in context: A097685 A136369 A305511 * A244272 A007573 A285663

Adjacent sequences:  A269469 A269470 A269471 * A269473 A269474 A269475

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Apr 13 2016

EXTENSIONS

Formula in name and last digit corrected by Vaclav Kotesovec, Jun 19 2020

STATUS

approved

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Last modified September 30 12:21 EDT 2020. Contains 337439 sequences. (Running on oeis4.)