A324836 Decimal expansion of eta_5, a constant related to the asymptotic density of certain sets of residues.

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

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-François Alcover, Mar 17 2019

Status

approved