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A175644 Decimal expansion of the sum 1/p^2 over primes p == 1 (mod 3). 3
0, 3, 3, 2, 1, 5, 5, 5, 0, 3, 2, 2, 2, 1, 7, 9, 5, 0, 5, 5, 2, 9, 2, 7, 1, 7, 7, 7, 8, 0, 1, 3, 8, 0, 9, 6, 4, 8, 1, 0, 8, 7, 5, 6, 6, 6, 5, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Prime Zeta modulo function at 2 for primes of the form 3k+1, which is sum_{primes = A002476} 1/p^2 = 1/7^2 +1/13^2 +1/19^2+ 1/31^2+...

The complementary sum_{primes = A003627} 1/p^2 is given by P_{3,2}(2) = A085548 - 1/3^2 - (this value here) = 0.307920758607736436842505075940...

LINKS

Table of n, a(n) for n=0..47.

R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT]

EXAMPLE

P_{3,1}(2) = 0.03321555032221795055292717778013809648108756665...

MATHEMATICA

(* A naive solution yielding 12 correct digits: *) s1 = s2 = 0.; Do[Switch[Mod[n, 3], 1, If[PrimeQ[n], s1 += 1/n^2], 2, If[PrimeQ[n], s2 += 1/n^2]], {n, 10^7}]; Join[{0}, RealDigits[(PrimeZetaP[2] + s1 - s2 - 1/9)/2, 10, 12][[1]]] (* Jean-Fran├žois Alcover, Mar 15 2018 *)

CROSSREFS

Cf. A086032, A175645.

Sequence in context: A038766 A080993 A140259 * A102905 A020862 A131589

Adjacent sequences:  A175641 A175642 A175643 * A175645 A175646 A175647

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Aug 01 2010

STATUS

approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)