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A324834
Decimal expansion of eta_3, a constant related to the asymptotic density of certain sets of residues.
7
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
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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved