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
Examples
0.12903892589780755649743486348177587763849321419920568830041270456398...
Links
- 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}
Programs
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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]
Formula
Sum_{p prime} 1/(p^2-1)^2.
Sum_{n>0} n P(2n+2) where P is the prime zeta P function.