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A343618 Decimal expansion of P_{3,2}(8) = Sum 1/p^8 over primes == 2 (mod 3). 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified October 6 20:00 EDT 2022. Contains 357270 sequences. (Running on oeis4.)