|
%I #14 Oct 11 2017 05:15:03
%S 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,
%T 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,
%U 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
%N 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.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, 2.3 Landau-Ramanujan Constant, p. 101.
%H Daniel Shanks, <a href="http://www.fq.math.ca/Scanned/13-4/shanks.pdf">Non-hypotenuse Numbers</a>, Fib. Quart., 13:4 (1975), pp. 319-321.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Landau-RamanujanConstant.html">Landau-Ramanujan Constant</a>
%e 0.973039776771781994254491281173646811...
%t 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 *)
%Y Cf. A004144, A009003, A064533, A088539.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Jul 04 2014
|
