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A175645 Decimal expansion of the sum 1/p^3 over primes == 1 (mod 3). 3
0, 0, 3, 6, 0, 0, 4, 2, 3, 3, 4, 6, 9, 4, 2, 9, 5, 8, 9, 5, 7, 4, 7, 6, 9, 4, 7, 6, 2, 9, 2, 3, 8, 4, 6, 4, 9, 4, 2, 4, 9, 5, 1, 6, 5, 1, 3, 6, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

The complementary sum_{primes = A003627} 1/p^3 is given by P_{3,2}(3) = A085541 - 1/3^3 - (this value here) = 0.13412517891546354042859932999943119899...

LINKS

Table of n, a(n) for n=0..48.

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}(3) = 0.00360042334694295895747694762923846494249516...

MATHEMATICA

(* A naive solution yielding 12 correct digits: *) s1 = s2 = 0.; Do[Switch[Mod[n, 3], 1, If[PrimeQ[n], s1 += 1/n^3], 2, If[PrimeQ[n], s2 += 1/n^3]], {n, 10^7}]; Join[{0, 0}, RealDigits[(PrimeZetaP[3] + s1 - s2 - 1/27)/2, 10, 12][[1]]] (* Jean-Fran├žois Alcover, Mar 15 2018 *)

CROSSREFS

Cf. A086033, A175644.

Sequence in context: A126334 A068635 A156695 * A178514 A154924 A071105

Adjacent sequences:  A175642 A175643 A175644 * A175646 A175647 A175648

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Aug 01 2010

STATUS

approved

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)