OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5. Kalmár’s Composition Constant, p. 293.
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
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Sep 23 2014
STATUS
approved