A343615 Decimal expansion of P_{3,2}(5) = Sum 1/p^5 over primes == 2 (mod 3).
0, 3, 1, 5, 7, 7, 1, 3, 5, 7, 1, 9, 0, 0, 3, 9, 4, 1, 9, 5, 6, 0, 3, 3, 7, 8, 0, 3, 4, 3, 7, 1, 6, 3, 9, 6, 3, 4, 7, 7, 7, 2, 9, 9, 6, 3, 8, 3, 2, 4, 8, 6, 1, 4, 5, 7, 9, 0, 2, 5, 8, 3, 4, 1, 2, 2, 8, 2, 9, 7, 5, 5, 7, 1, 9, 8, 1, 1, 7, 3, 0, 3, 9, 1, 5, 9, 6, 1, 1, 0, 7, 5, 2, 9, 7, 6, 2, 6, 2
Offset: 0
Examples
0.0315771357190039419560337803437163963477729963832486145790258341228297557...
Links
- R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015, value P(m=3, n=2, s=5) on p. 21.
- OEIS index to entries related to the (prime) zeta function.
Crossrefs
Programs
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PARI
s=0;forprimestep(p=2,1e8,3,s+=1./p^4);s \\ For illustration: using primes up to 10^N gives about 3N+2 (= 26 for N=8) correct digits.
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PARI
A343615_upto(N=100, s=5)={localprec(N+5); digits((sumeulerrat(1/p^s)-1/3^s-PrimeZeta31(s)+1)\.1^N)[^1]} \\ see A175644 for the function PrimeZeta31, A343612 for a function PrimeZeta32
Formula
P_{3,2}(5) = P(5) - 1/3^5 - P_{3,1}(5).
Comments