A324834 Decimal expansion of eta_3, a constant related to the asymptotic density of certain sets of residues.

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

Offset

-1,1

Links

Table of n, a(n) for n=-1..100.

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)^3.

Sum_{n>0} (n(n+1)/2) P(2n+4) where P is the prime zeta P function.

Example

0.03907240573557479188765950332042297638668483824477336035675406603269...

Mathematica

digits = 102; m0 = 2 digits; Clear[rd]; rd[m_] := rd[m] = RealDigits[eta3 = Sum[n (n+1)/2 PrimeZetaP[2 n + 4], {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[eta3, digits]]; rd[m]

Crossrefs

Cf. A154945 (eta_1), A324833 (eta_2), A324835 (eta_4), A324836 (eta_5).

Sequence in context: A134878 A339097 A154540 * A019832 A244337 A338033

Adjacent sequences: A324831 A324832 A324833 * A324835 A324836 A324837

Keyword

nonn,cons

Author

Jean-François Alcover, Mar 17 2019

Status

approved