A071705 Least k > n such that C(2n,n) divides C(2k,k).

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

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}]
lk[n_]:=Module[{k=n+1, c=Binomial[2n, n]}, While[Mod[Binomial[2k, k], c]!=0, k++]; k]; Array[lk, 60, 0] (* Harvey P. Dale, Apr 02 2022 *)

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: A038707 A290140 A109853 * 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