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A286229 Decimal expansion of Sum_{p prime} 1/(p^3 - 1). 1
1, 9, 4, 1, 1, 8, 1, 6, 9, 8, 3, 2, 6, 3, 3, 7, 9, 2, 2, 9, 9, 5, 8, 7, 4, 8, 4, 9, 1, 1, 3, 8, 0, 8, 3, 7, 4, 5, 1, 8, 7, 7, 0, 1, 8, 4, 5, 2, 7, 9, 2, 1, 9, 7, 7, 3, 5, 0, 4, 3, 4, 9, 4, 0, 4, 1, 0, 3, 8, 0, 8, 7, 4, 2, 0, 5, 7, 9, 2, 5, 2, 6, 3, 3, 9, 3, 9, 5, 3, 9, 8, 7, 7, 6, 5, 4, 3, 5, 3, 6, 7, 8, 8, 2, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Eric Weisstein's World of Mathematics, Prime Zeta Function.

Eric Weisstein's World of Mathematics, Prime Sums.

FORMULA

Equals Sum_{k>=1} primezeta(3*k).

More generally, Sum_{p prime} 1/(p^s - 1) = Sum_{k>=1} primezeta(s*k).

EXAMPLE

1/(2^3 - 1) + 1/(3^3 - 1) + 1/(5^3 - 1) + ... = 1/2^3 + 1/3^3 + 1/5^3 + ... + 1/2^6 + 1/3^6 + 1/5^6 + ... + 1/2^9 + 1/3^9 + 1/5^9 + ... = 0.19411816983263379229...

MATHEMATICA

digits = 105; sp = NSum[PrimeZetaP[3 n], {n, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 2*digits]; RealDigits[sp, 10, digits] // First

PROG

(PARI) sumeulerrat(1/(p^3-1)) \\ Amiram Eldar, Mar 18 2021

CROSSREFS

Cf. A030078, A085541, A154945.

Sequence in context: A270309 A010158 A336274 * A242611 A098454 A298531

Adjacent sequences:  A286226 A286227 A286228 * A286230 A286231 A286232

KEYWORD

nonn,cons

AUTHOR

Ilya Gutkovskiy, May 04 2017

STATUS

approved

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Last modified May 6 04:43 EDT 2021. Contains 343580 sequences. (Running on oeis4.)