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 A071705 Least k > n such that C(2n,n) divides C(2k,k). 1
 1, 2, 5, 9, 13, 20, 18, 21, 20, 63, 50, 131, 111, 67, 197, 113, 113, 338, 335, 173, 426, 110, 110, 554, 515, 515, 368, 368, 515, 928, 928, 1269, 1152, 1152, 1269, 1511, 1462, 1456, 1458, 1458, 2524, 2181, 2895, 2895, 2895, 2805, 3379, 3379, 3640, 2808, 3284 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Erdős proved that a(n) >= 2n, and that there is a constant c > 0 such that for sufficient large n, n^(1+c) < a(n) < (2n)^(log(n)/log(2)). - Amiram Eldar, May 18 2017 LINKS Giovanni Resta, Table of n, a(n) for n = 0..600 Paul Erdős, On some divisibility properties of (2n n), Canadian Mathematical Bulletin, Vol. 7, No. 4 (1964), pp. 513-518. MATHEMATICA f[n_] := Block[{k = n + 1}, bn = Binomial[2n, n]; While[ !IntegerQ[ Binomial[2k, k]/bn], k++ ]; k]; Table[ f[n], {n, 0, 50}] PROG (PARI) for(n=1, 45, s=n+1; while(binomial(2*s, s)%binomial(2*n, n)>0, s++); print1(s, ", ")) CROSSREFS Sequence in context: A120615 A038707 A290140 * A281171 A190713 A288347 Adjacent sequences:  A071702 A071703 A071704 * A071706 A071707 A071708 KEYWORD nonn AUTHOR Benoit Cloitre, Jun 24 2002 EXTENSIONS Edited by Robert G. Wilson v, Jun 27 2002 STATUS approved

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Last modified February 16 20:45 EST 2019. Contains 320189 sequences. (Running on oeis4.)