A081767 Numbers k such that k^2 - 1 divides binomial(2k,k).

2, 16, 21, 29, 43, 46, 67, 78, 89, 92, 105, 111, 141, 154, 157, 171, 188, 191, 205, 210, 211, 221, 229, 232, 239, 241, 267, 277, 300, 309, 313, 316, 323, 326, 331, 346, 369, 379, 415, 421, 430, 436, 441, 443, 451, 460, 461, 465, 469, 477, 484, 494, 497, 528

Offset

1,1

Comments

Is a(n) asymptotic to c*n with 9 < c < 10?

A subset of A004782: numbers k such that 2(2k-3)!/(k!(k-1)!) is an integer.

Equivalently, numbers k such that k-1 divides A000108(k), the k-th Catalan number. - M. F. Hasler, Nov 11 2015

The data does not appear to support the conjectured asymptote statement (neither the constant nor being linear). - Bill McEachen, Feb 26 2024

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems, sect. III: Binomial coefficients modulo integers, binomod.gp (v.1.4, 11/2015).

Mathematica

Select[Range[2, 600], Divisible[Binomial[2#, #], #^2-1]&] (* Harvey P. Dale, May 11 2013 *)

Prog

(PARI) for(n=2, 999, binomial(2*n, n)%(n^2-1)||print1(n", ")) \\ M. F. Hasler, Nov 11 2015
(PARI) is_A081767(n)=!binomod(2*n, n, n^2-1) \\ Using binomod.gp by Max Alekseyev, cf. links. - M. F. Hasler, Nov 11 2015

Crossrefs

Subsequence of A094575 and of A004782.

Cf. A000108.

Sequence in context: A050850 A082475 A333998 * A093026 A271627 A118954

Adjacent sequences: A081764 A081765 A081766 * A081768 A081769 A081770

Keyword

nonn

Author

Benoit Cloitre, Apr 09 2003

Status

approved