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%I #11 Jul 18 2017 12:11:53
%S 3,5,6,7,8,9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,29,30,
%T 31,32,33,34,35,37,38,39,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
%U 56,59,60,61,62,63,64,65,67,68,69,71,72,73,74,75,76,77
%N Numbers n such that binomial(2*n,n) < (2*n)^pi(n).
%C Ecklund and Eggleton proved that binomial(n,k) > n^pi(k) for n >= 2k and k >= 202, where pi(k) = A000720(k). Therefore this sequence is finite.
%H Amiram Eldar, <a href="/A289178/b289178.txt">Table of n, a(n) for n = 1..104</a>
%H Earl F. Ecklund, Jr. and Roger B. Eggleton, <a href="http://www.jstor.org/stable/2317422">Prime factors of consecutive integers</a>, The American Mathematical Monthly, Vol. 79, No. 10 (1972), pp. 1082-1089.
%t binomQ[n_] := Binomial[2n, n] < (2n)^PrimePi[n]; Select[Range[250], binomQ]
%o (PARI) isok(n) = binomial(2*n,n) < (2*n)^primepi(n); \\ _Michel Marcus_, Jun 28 2017
%Y Cf. A000720, A000984.
%K nonn,fini,full
%O 1,1
%A _Amiram Eldar_, Jun 27 2017
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