A143071 A positive integer n is included if the number of 1's in the binary representation of n is a power of 2 (including being possibly 1).

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 23, 24, 27, 29, 30, 32, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 64, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 85, 86, 89, 90, 92, 96, 99, 101, 102, 105, 106, 108, 113, 114, 116, 120, 128, 129, 130, 132, 135

Offset: 1

Author

Leroy Quet, Jul 22 2008

Keywords

• base
• nonn

Examples

			34 in binary is 100010. This has 2 ones. And since 2 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. A000120, A143070, A143072, A209229.

For complement see A271499.

Programs

Haskell

a143071 n = a143071_list !! (n-1)
a143071_list = filter ((== 1) . a209229 . a000120) [1..]
-- Reinhard Zumkeller, Sep 14 2014

Maple

a:=proc(n) local nn, n1: nn:=convert(n,base,2): n1:=add(nn[j],j=1..nops(nn)): if 0 < n1 and type(log[2](n1),integer)=true then n else end if end proc: seq(a(n),n=1..140); # Emeric Deutsch, Aug 13 2008

Mathematica

Select[Range[150],IntegerQ[Log2[DigitCount[#,2,1]]]&] (* Harvey P. Dale, Sep 26 2020 *)

Formula

A209229(A000120(a(n))) = 1. - Reinhard Zumkeller, Sep 14 2014

Extensions

More terms from Emeric Deutsch, Aug 13 2008