%I #8 Feb 24 2018 14:03:21

%S 2,5,19,6299,35743868,4259425108512909,

%T 41287268337787979739179113461425,

%U 8252465584213549846948406832722177155507422403521413106477917012

%N Denominators of r-Egyptian fraction expansion for the Euler-Mascheroni constant (EulerGamma), where r(k) = 1/(2k-1).

%C Suppose that r is a sequence of rational numbers r(k) <= 1 for k >= 1, and that x is an irrational number in (0,1). Let f(0) = x, n(k) = floor(r(k)/f(k-1)), and f(k) = f(k-1) - r(k)/n(k). Then x = r(1)/n(1) + r(2)/n(2) + r(3)/n(3) + ... , the r-Egyptian fraction for x.

%C See A269993 for a guide to related sequences.

%H Clark Kimberling, <a href="/A270556/b270556.txt">Table of n, a(n) for n = 1..11</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%e Euler-Mascheroni constant = 1/(1*2) + 1/(3*5) + 1/(5*19) + 1/(7*6299) + ...

%t r[k_] := 1/(2k-1); f[x_, 0] = x; z = 10;

%t n[x_, k_] := n[x, k] = Ceiling[r[k]/f[x, k - 1]]

%t f[x_, k_] := f[x, k] = f[x, k - 1] - r[k]/n[x, k]

%t x = EulerGamma; Table[n[x, k], {k, 1, z}]

%Y Cf. A269993, A005408.

%K nonn,frac,easy

%O 1,1

%A _Clark Kimberling_, Apr 03 2016