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

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, 2.3 Landau-Ramanujan Constant, p. 101.

Links

Table of n, a(n) for n=0..99.

Daniel Shanks, Non-hypotenuse Numbers, Fib. Quart., 13:4 (1975), pp. 319-321.

Eric Weisstein's MathWorld, Landau-Ramanujan Constant

Example

0.973039776771781994254491281173646811...

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 *)

Crossrefs

Cf. A004144, A009003, A064533, A088539.

Sequence in context: A197834 A173515 A091558 * A307229 A002205 A363766

Adjacent sequences: A244656 A244657 A244658 * A244660 A244661 A244662

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 04 2014

Status

approved