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%I #18 Jan 21 2016 11:24:03
%S 3,5,5,3,3,3,3,5,11,3,7,5,3,3,3,3,3,3,3,3,3,3,3,3,3,7,5,3,7,7,3,3,3,3,
%T 7,7,3,5,5,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%U 3,3,3,3,3,3,3,3,3,3,3,5,5,3,5,5,3,3,3,3,5,5,3,5,5,3,3,3,3,3,3,3,3,3,3,3,3
%N Smallest odd prime dividing binomial(2n,n).
%C The Erdős paper calls this function g(n) and states that it not known whether it is bounded. Currently, g(3160)=13 is the greatest known value of g. See A129489.
%H T. D. Noe, <a href="/A129488/b129488.txt">Table of n, a(n) for n = 2..5000</a>
%H P. Erdős, R. L. Graham, I. Z. Russa and E. G. Straus, <a href="http://dx.doi.org/10.1090/S0025-5718-1975-0369288-3">On the prime factors of C(2n,n)</a>, Math. Comp. 29 (1975), 83-92.
%t Table[Transpose[FactorInteger[Binomial[2n,n]]][[1,2]], {n,2,150}]
%o (PARI) a(n)=my(k);forprime(p=3,default(primelimit),k=1;while((k*=p)<=2*n,if(n/k-n\k>1/2,return(p)))) \\ _Charles R Greathouse IV_, Dec 19 2011
%Y Cf. A030979 (n such that g(n)>=11), A129489, A266366.
%K nonn
%O 2,1
%A _T. D. Noe_, Apr 17 2007