A247818 Decimal expansion of 1/(theta*P'(theta)), a constant appearing in the asymptotic evaluation of the coefficients q_n in 1/(1+P(x)), where P(x) is the generating function of the primes and theta the unique zero of P(x) in [-3/4, 0].

6, 2, 2, 3, 0, 6, 5, 7, 4, 5, 7, 0, 0, 8, 5, 6, 6, 4, 6, 2, 1, 3, 4, 1, 1, 8, 1, 2, 7, 0, 0, 0, 9, 6, 0, 5, 1, 3, 0, 7, 8, 4, 3, 0, 1, 4, 7, 9, 0, 0, 7, 8, 5, 4, 2, 0, 3, 7, 4, 7, 2, 8, 1, 5, 6, 2, 4, 6, 0, 4, 6, 7, 8, 6, 9, 4, 6, 2, 4, 0, 8, 4, 8, 9, 4, 6, 3, 5, 8, 8, 2, 2, 0, 8, 7, 6, 3, 6, 8, 2

Offset: 0

Author

Jean-François Alcover, Sep 24 2014

Keywords

• nonn
• cons

Examples

			-0.622306574570085664621341181270009605130784301479...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5. Kalmár’s Composition Constant, p. 294 and p. 551.

Crossrefs

Cf. A030018, A072508, A088751.

Programs

Mathematica

digits = 100; P[x_] := 1 + Sum[Prime[n]*x^n, {n, 1, 1000}]; PPrime[x_] := Sum[n*Prime[n]*x^(n-1), {n, 1, 1000}]; theta = x /. FindRoot[P[x] == 0, {x, -3/4}, WorkingPrecision -> digits+5]; RealDigits[1/(theta*PPrime[theta]), 10, digits] // First

Formula

q_n ~ (1/(theta*P'(theta))) * (1/theta^n).