The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A343618 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A343618

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

#12 by Susanna Cuyler at Mon Apr 26 06:34:36 EDT 2021

STATUS

reviewed

approved

#11 by Joerg Arndt at Mon Apr 26 04:39:58 EDT 2021

STATUS

proposed

reviewed

#10 by Michel Marcus at Mon Apr 26 04:24:02 EDT 2021

STATUS

editing

proposed

#9 by Michel Marcus at Mon Apr 26 04:23:59 EDT 2021

FORMULA

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

STATUS

reviewed

editing

#8 by Joerg Arndt at Mon Apr 26 04:18:20 EDT 2021

STATUS

proposed

reviewed

#7 by Michel Marcus at Mon Apr 26 04:10:49 EDT 2021

STATUS

editing

proposed

#6 by Michel Marcus at Mon Apr 26 04:10:46 EDT 2021

LINKS

R. J. Mathar, <a href="http://arxiv.org/abs/1008.2547">Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli</a>, arXiv:1008.2547 [math.NT], 2010-2015, value P(m=3, n=2, s=8), p. 21.

STATUS

approved

editing

#5 by M. F. Hasler at Mon Apr 26 03:37:21 EDT 2021

STATUS

editing

approved

#4 by M. F. Hasler at Mon Apr 26 01:36:57 EDT 2021

DATA

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

EXAMPLE

0.0078253541130504928742517016707559206033079309751324433146804883394003908814823388594971406115663072323981226161069324694978359864189332...

#3 by M. F. Hasler at Mon Apr 26 01:33:07 EDT 2021

FORMULA

P_{3,2}(78) = Sum_{p in A003627} 1/p^8 = P(8) - 1/3^8 - P_{3,1}(8)

CROSSREFS

Cf. A003627 (primes 3k-1), A001016 (n^78), A085968 (PrimeZeta(78)).