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

1,1

Links

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

Formula

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

Example

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

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 *)

Prog

(Haskell)
a143070 n = a143070_list !! (n-1)
a143070_list = filter ((== 1) . a209229 . a023416) [1..]
-- Reinhard Zumkeller, Sep 14 2014
(PARI) ispow2(n) = (n==1) || (n==2) || (ispower(n, , &k) && (k==2));
isok(n) = ispow2(#binary(n) - hammingweight(n)); \\ Michel Marcus, Oct 26 2017

Crossrefs

Cf. A023416, A143071, A143072.

Cf. A209229.

Sequence in context: A072726 A343585 A153242 * A340698 A206926 A005528

Adjacent sequences: A143067 A143068 A143069 * A143071 A143072 A143073

Keyword

base,nonn

Author

Leroy Quet, Jul 22 2008

Extensions

More terms from Emeric Deutsch, Aug 11 2008

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

Status

approved