A042943 - OEIS

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

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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