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A324836 Decimal expansion of eta_5, a constant related to the asymptotic density of certain sets of residues. 5
4, 1, 4, 5, 8, 7, 3, 4, 7, 5, 2, 5, 8, 9, 5, 6, 1, 9, 5, 3, 2, 4, 6, 7, 8, 8, 7, 0, 5, 9, 0, 5, 1, 7, 8, 1, 7, 5, 4, 1, 9, 3, 1, 4, 0, 5, 6, 2, 2, 8, 7, 9, 2, 9, 9, 5, 5, 7, 8, 8, 1, 3, 1, 2, 8, 0, 6, 4, 9, 6, 5, 3, 8, 8, 4, 7, 0, 0, 9, 6, 9, 7, 9, 1, 4, 6, 8, 1, 6, 9, 9, 7, 8, 5, 5, 0, 3, 5, 1, 4, 7, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

-2,1

LINKS

Table of n, a(n) for n=-2..99.

Carl Pomerance, Andrzej Schinzel, Multiplicative Properties of Sets of Residues, Moscow Journal of Combinatorics and Number Theory. 2011. Vol. 1. Iss. 1. pp. 52-66. See p. 62.

FORMULA

Sum_{p prime} 1/(p^2-1)^5.

Sum_{n>0} (n(n-1)(n-2)(n-3)/24) P(2n+2) where P is the prime zeta P function.

EXAMPLE

0.0041458734752589561953246788705905178175419314056228792995578813128...

MATHEMATICA

digits = 102; m0 = 2 digits; Clear[rd]; rd[m_] := rd[m] = RealDigits[eta5 = Sum[n(n-1)(n-2)(n-3)/24 PrimeZetaP[2n+2], {n, 1, m}], 10, digits][[1]]; rd[m0]; rd[m = 2 m0]; While[rd[m] != rd[m - m0], Print[m]; m = m + m0]; Print[N[eta5, digits]]; rd[m]

CROSSREFS

Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3), A324835 (eta_4).

Sequence in context: A093561 A286327 A081773 * A302151 A167431 A205848

Adjacent sequences:  A324833 A324834 A324835 * A324837 A324838 A324839

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Mar 17 2019

STATUS

approved

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Last modified January 25 00:44 EST 2022. Contains 350565 sequences. (Running on oeis4.)