A042943 Numbers k such that binomial(2^k, k) is divisible by binomial(2^k, 2).

1, 2, 3, 5, 7, 9, 11, 13, 14, 17, 19, 22, 23, 25, 26, 27, 29, 31, 33, 35, 37, 38, 39, 41, 43, 45, 46, 47, 49, 50, 51, 53, 55, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 79, 81, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 98, 99, 101, 102, 103, 106, 107, 109, 111

Offset

1,2

Comments

Does not contain multiples of 4 (A008586).

Links

Table of n, a(n) for n=1..68.

Formula

k : A014070(k) mod A006516(k) = binomial(2^k, k) mod binomial(2^n, 2) = 0.

Mathematica

Select[Range[150], Divisible[Binomial[2^#, #], Binomial[2^#, 2]]&]  (* Harvey P. Dale, Mar 24 2011 *)

Prog

(PARI) isok(k) = (binomial(2^k, k) % binomial(2^k, 2)) == 0; \\ Michel Marcus, May 14 2018

Crossrefs

Cf. A014070, A006516.

Sequence in context: A079051 A226047 A066935 * A306466 A258037 A186330

Adjacent sequences: A042940 A042941 A042942 * A042944 A042945 A042946

Keyword

easy,nonn

Author

Labos Elemer, Apr 11 2001

Status

approved