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%I #8 Feb 24 2018 11:53:50
%S 2,5,122,36864,13343376668,224851808819852270264,
%T 206030526699009549783863692475305411157116,
%U 42500635870294544529750048452464143848264977426702636517113215245943832312921983097
%N Denominators of r-Egyptian fraction expansion for 1/Pi, where r(k) = 1/Prime(k).
%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="/A270481/b270481.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 1/Pi = 1/(2*2) + 1/(3*5) + 1/(5*122) + 1/(7*36864) + ...
%t r[k_] := 1/Prime[k]; 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 = 1/Pi; Table[n[x, k], {k, 1, z}]
%Y Cf. A269993, A000040.
%K nonn,frac,easy
%O 1,1
%A _Clark Kimberling_, Mar 30 2016
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