A244659 Decimal expansion of 4*K/Pi, a constant appearing in the asymptotic evaluation of the number of non-hypotenuse numbers not exceeding a given bound, where K is the Landau-Ramanujan constant.
9, 7, 3, 0, 3, 9, 7, 7, 6, 7, 7, 1, 7, 8, 1, 9, 9, 4, 2, 5, 4, 4, 9, 1, 2, 8, 1, 1, 7, 3, 6, 4, 6, 8, 1, 1, 0, 7, 6, 3, 4, 3, 9, 6, 3, 4, 7, 9, 0, 8, 2, 4, 2, 7, 3, 7, 6, 3, 0, 9, 0, 2, 1, 6, 3, 2, 5, 9, 7, 1, 0, 1, 8, 6, 4, 1, 5, 1, 6, 3, 4, 2, 9, 5, 2, 0, 4, 0, 4, 2, 0, 7, 6, 2, 1, 3, 8, 7, 4, 2
Offset: 0
Examples
0.973039776771781994254491281173646811...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, 2.3 Landau-Ramanujan Constant, p. 101.
Links
- Daniel Shanks, Non-hypotenuse Numbers, Fib. Quart., 13:4 (1975), pp. 319-321.
- Eric Weisstein's MathWorld, Landau-Ramanujan Constant
Programs
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Mathematica
digits = 100; LandauRamanujan[n_] := With[{K = Ceiling[Log[2, n*Log[3, 10]]]}, N[Product[(((1-2^(-2^k))*4^2^k*Zeta[2^k])/(Zeta[2^k, 1/4] - Zeta[2^k, 3/4]))^2^(-k-1), {k, 1, K}]/Sqrt[2], n]]; K = LandauRamanujan[digits+5]; RealDigits[4*K/Pi, 10, digits] // First (* after Victor Adamchik *)