A143070 A positive integer n is included if the number of 0's in the binary representation of n is a power of 2 (including being possibly 1).

2, 4, 5, 6, 9, 10, 11, 12, 13, 14, 16, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 47, 48, 51, 53, 54, 55, 57, 58, 59, 60, 61, 62, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 95, 97, 98, 100, 103, 104, 107, 109, 110, 111, 112, 115

Offset: 1

Author

Leroy Quet, Jul 22 2008

Keywords

• base
• nonn

Examples

			34 in binary is 100010. This has 4 zeros. And since 4 is a power of 2, 34 is included in the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023416, A143071, A143072.

Cf. A209229.

Programs

Haskell

a143070 n = a143070_list !! (n-1)
a143070_list = filter ((== 1) . a209229 . a023416) [1..]
-- Reinhard Zumkeller, Sep 14 2014

Maple

a:=proc(n) local nn,n0: nn:=convert(n,base,2): n0:=nops(nn)-add(nn[j], j=1.. nops(nn)): if 0 < n0 and type(log[2](n0),integer)=true then n else end if end proc: seq(a(n),n=1..100); # Emeric Deutsch, Aug 11 2008

Mathematica

Select[Range@ 120, IntegerQ@ Log2@ DigitCount[#, 2, 0] &] (* Michael De Vlieger, Oct 25 2017 *)

PARI

ispow2(n) = (n==1) || (n==2) || (ispower(n,,&k) && (k==2));
isok(n) = ispow2(#binary(n) - hammingweight(n)); \\ Michel Marcus, Oct 26 2017

Formula

A209229(A023416(a(n))) = 1. - Reinhard Zumkeller, Sep 14 2014

Extensions

More terms from Emeric Deutsch, Aug 11 2008

a(61)-a(68) from Ray Chandler, Jun 20 2009