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 A324835 Decimal expansion of eta_4, a constant related to the asymptotic density of certain sets of residues. 4
 1, 2, 5, 9, 3, 0, 2, 8, 3, 9, 8, 6, 4, 2, 0, 1, 3, 6, 5, 2, 9, 9, 1, 1, 0, 2, 2, 6, 2, 2, 9, 2, 1, 7, 6, 9, 4, 7, 3, 4, 3, 2, 0, 8, 9, 8, 5, 4, 2, 2, 1, 8, 6, 1, 4, 7, 2, 5, 7, 8, 9, 3, 6, 6, 9, 5, 4, 7, 5, 7, 7, 9, 0, 8, 4, 7, 0, 9, 9, 1, 8, 3, 2, 8, 4, 7, 7, 0, 8, 9, 7, 8, 5, 9, 1, 1, 0, 1, 3, 9, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET -1,2 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)^4. Sum_{n>0} (n(n+1)(n+2)/6) P(2n+6) where P is the prime zeta P function. EXAMPLE 0.0125930283986420136529911022622921769473432089854221861472578936695... MATHEMATICA digits = 101; m0 = 2 digits; Clear[rd]; rd[m_] := rd[m] = RealDigits[eta4 = Sum[n(n+1)(n+2)/6 PrimeZetaP[2n+6], {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[eta4, digits]]; rd[m] CROSSREFS Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3), A324836 (eta_5). Sequence in context: A019802 A248934 A011432 * A082183 A111474 A111761 Adjacent sequences:  A324832 A324833 A324834 * A324836 A324837 A324838 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Mar 17 2019 STATUS approved

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Last modified January 24 07:18 EST 2020. Contains 331189 sequences. (Running on oeis4.)