A324833 Decimal expansion of eta_2, a constant related to the asymptotic density of certain sets of residues.

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

Offset

0,2

Links

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

Index to constants which are prime zeta sums {0,2,2}

Formula

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

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

Equals - A136141/4 + A086242/4 - A179119/4 + A382554/4. - Artur Jasinski, Mar 31 2025

Example

0.12903892589780755649743486348177587763849321419920568830041270456398...

Mathematica

digits = 101; m0 = 2 digits; Clear[rd]; rd[m_] := rd[m] = RealDigits[eta2 = Sum[n PrimeZetaP[2n + 2], {n, 1, m}], 10, digits][[1]]; rd[m0]; rd[m = 2m0]; While[rd[m] != rd[m-m0], Print[m]; m = m+m0]; Print[N[eta2, digits] ]; rd[m]

Crossrefs

Cf. A154945 (eta_1), A324834 (eta_3), A324835 (eta_4), A324836 (eta_5).

Sequence in context: A021779 A201893 A264920 * A019969 A185362 A140239

Adjacent sequences: A324830 A324831 A324832 * A324834 A324835 A324836

Keyword

nonn,cons

Author

Jean-François Alcover, Mar 17 2019

Status

approved