A247734 Decimal expansion of the coefficient c appearing in the asymptotic evaluation of the number of prime additive compositions of n as c*(1/xi)^n, where xi is A084256.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5. Kalmár’s Composition Constant, p. 293.

Links

Table of n, a(n) for n=0..101.

Formula

c = 1/(xi*f'(xi)), where f(x) is the sum over primes x^2 + x^3 + x^5 + x^7 + ..., xi (A084256) being the positive solution of f(x) = 1.

Example

0.3036552633952545488542057678902065632735...
1/xi = 1.4762287836208969657929439948482332947971...

Mathematica

nMax = 200; digits = 102; f[x_] := Sum[x^Prime[n], {n, 1, nMax}]; fp[x_] := Sum[Prime[n]*x^(Prime[n] - 1), {n, 1, nMax}]; xi = x /. FindRoot[f[x] == 1, {x, 2/3}, WorkingPrecision -> digits+5]; c = 1/(xi*fp[xi]); RealDigits[c, 10, digits] // First

Crossrefs

Cf. A084256 (xi).

Sequence in context: A282610 A011076 A200278 * A010599 A226568 A038517

Adjacent sequences: A247731 A247732 A247733 * A247735 A247736 A247737

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 23 2014

Status

approved