cp's OEIS Frontend

A243584 Decimal expansion of 1/(eta*P'(eta)), a constant related to the asymptotic evaluation of the number of prime multiplicative compositions, where eta is A243350, the unique solution of P(x)=1, P being the prime zeta P function (P(x) = sum_(p prime) 1/p^x).

%I A243584 #10 Feb 16 2025 08:33:22
%S A243584 4,1,2,7,7,3,2,3,7,0,9,3,6,7,0,4,8,7,2,8,9,0,4,2,6,9,9,1,7,2
%N A243584 Decimal expansion of 1/(eta*P'(eta)), a constant related to the asymptotic evaluation of the number of prime multiplicative compositions, where eta is A243350, the unique solution of P(x)=1, P being the prime zeta P function (P(x) = sum_(p prime) 1/p^x).
%D A243584 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5 Kalmar's composition constant, p. 293.
%H A243584 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta function</a>
%e A243584 0.41277323709367...
%t A243584 digits = 30; eta = x /. FindRoot[PrimeZetaP[x] == 1, {x, 7/5},  WorkingPrecision -> digits + 200]; c = N[1/(eta*PrimeZetaP'[eta]) // Re, digits + 200]; RealDigits[c, 10, digits ] // First (* updated Sep 11 2015 *)
%Y A243584 Cf. A243350.
%K A243584 nonn,cons,more
%O A243584 0,1
%A A243584 _Jean-François Alcover_, Jun 06 2014