A129488 Smallest odd prime dividing binomial(2n,n).

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, 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, 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

Offset

2,1

Comments

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.

Links

T. D. Noe, Table of n, a(n) for n = 2..5000

P. Erdős, R. L. Graham, I. Z. Russa and E. G. Straus, On the prime factors of C(2n,n), Math. Comp. 29 (1975), 83-92.

Mathematica

Table[Transpose[FactorInteger[Binomial[2n, n]]][[1, 2]], {n, 2, 150}]

Prog

(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

Crossrefs

Cf. A030979 (n such that g(n)>=11), A129489, A266366.

Sequence in context: A110551 A141334 A199614 * A211023 A279494 A053670

Adjacent sequences: A129485 A129486 A129487 * A129489 A129490 A129491

Keyword

nonn

Author

T. D. Noe, Apr 17 2007

Status

approved