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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).
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%I #9 Sep 11 2015 08:29:02

%S 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 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 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5 Kalmar's composition constant, p. 293.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta function</a>

%e 0.41277323709367...

%t 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 Cf. A243350.

%K nonn,cons,more

%O 0,1

%A _Jean-François Alcover_, Jun 06 2014