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%I #19 Jul 11 2022 08:36:39
%S 2,10,127,18838,522338493,727608914652776081,
%T 990935377560451600699026552443764271,
%U 1223212384013602554473872691328685513734082755736750146553750539914774364
%N Denominators of an Egyptian fraction for 1/zeta(2) = 0.607927101854... (A059956).
%H Amiram Eldar, <a href="/A144835/b144835.txt">Table of n, a(n) for n = 1..11</a>
%H Mohammad K. Azarian, <a href="http://www.jstor.org/stable/10.4169/college.math.j.42.4.329">Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958</a>, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. <a href="http://www.jstor.org/stable/10.4169/college.math.j.43.4.337">Solution</a> published in Vol. 43, No. 4, September 2012, pp. 340-342.
%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/zeta(2) = 0.607927101854... = 1/2 + 1/10 + 1/127 + 1/18838 + ...
%t a = {}; k = N[1/Zeta[2], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a
%o (PARI) x=1/zeta(2); while(x, t=1\x+1; print1(t", "); x -= 1/t) \\ _Charles R Greathouse IV_, Nov 08 2013
%Y Cf. A001466, A006487, A006524, A006525, A006526, A059956, A069139, A110820, A117116, A118323, A118324, A118325.
%K frac,nonn
%O 1,1
%A _Artur Jasinski_, Sep 22 2008
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