A213594 Greatest number k such that A048784(n) / 2^k is an integer.

1, 2, 1, 3, 1, 3, 5, 4, 4, 4, 7, 5, 6, 7, 5, 7, 8, 7, 9, 8, 11, 11, 8, 7, 9, 11, 8, 13, 12, 11, 12, 11, 12, 12, 14, 13, 15, 15, 11, 13, 14, 18, 15, 15, 15, 14, 17, 14, 17, 18, 18, 20, 17, 19, 19, 19, 18, 19, 21, 19, 19, 21, 20, 22, 18, 21, 24, 22, 26, 24, 20

Offset: 1

Author

Michel Lagneau, Jun 15 2012

Keywords

• nonn

Comments

2-adic valuation of A048784.

Property: a(n) > 0, that is A048784(n) is even, for n > 0.

Examples

			a(7) = 5 because A048784(7) / 2^5 = 32 / 32 = 1 is an integer.
		

Links

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

Crossrefs

Cf. A000005, A048784.

Programs

Maple

with(numtheory): for n from 1 to 100 do:ii:=0:for k from 500 by -1 to 1 while(ii=0) do: x:=evalf(tau(binomial(2*n,n))/2^k):if x=floor(x) then ii:=1: printf(`%d, `,k):else fi:od:od:

PARI

a(n)=valuation(numdiv(binomial(2*n,n)),2) \\ Charles R Greathouse IV, Jun 15 2012