A343618 - OEIS

A343618

Decimal expansion of P_{3,2}(8) = Sum 1/p^8 over primes == 2 (mod 3).

0, 0, 3, 9, 0, 8, 8, 1, 4, 8, 2, 3, 3, 8, 8, 5, 9, 4, 9, 7, 1, 4, 0, 6, 1, 1, 5, 6, 6, 3, 0, 7, 2, 3, 2, 3, 9, 8, 1, 2, 2, 6, 1, 6, 1, 0, 6, 9, 3, 2, 4, 6, 9, 4, 9, 7, 8, 3, 5, 9, 8, 6, 4, 1, 8, 9, 3, 3, 2, 1, 7, 9, 5, 8, 6, 3, 0, 3, 3, 6, 9, 7, 1, 5, 5, 9, 6, 1, 7, 2, 6, 0, 4, 3, 1, 8, 3, 0, 8, 9, 2, 7, 6, 5, 9

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OFFSET

0,3

COMMENTS

The prime zeta modulo function P_{m,r}(s) = Sum_{primes p == r (mod m)} 1/p^s generalizes the prime zeta function P(s) = Sum_{primes p} 1/p^s.

LINKS

Table of n, a(n) for n=0..104.

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=8), p. 21.

OEIS index to entries related to the (prime) zeta function.

FORMULA

P_{3,2}(8) = Sum_{p in A003627} 1/p^8 = P(8) - 1/3^8 - P_{3,1}(8).

EXAMPLE

0.003908814823388594971406115663072323981226161069324694978359864189332...

PROG

(PARI) A343618_upto(N=100)={localprec(N+5); digits((PrimeZeta32(8)+1)\.1^N)[^1]} \\ see A343612 for the function PrimeZeta32

CROSSREFS

Cf. A003627 (primes 3k-1), A001016 (n^8), A085968 (PrimeZeta(8)).

Cf. A343612 - A343619 (P_{3,2}(s): analog for 1/p^s, s = 2 .. 9).

Cf. A343628 (for primes 3k+1), A086038 (for primes 4k+1), A085997 (for primes 4k+3).

Sequence in context: A011337 A195456 A021723 * A206160 A112972 A334191

Adjacent sequences: A343615 A343616 A343617 * A343619 A343620 A343621

KEYWORD

nonn,cons

AUTHOR

M. F. Hasler, Apr 25 2021

STATUS

approved