A143072 -id:A143072 - cp's OEIS frontend

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

Leroy Quet, Jul 22 2008

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

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

Cf. A000120, A143070, A143072, A209229.

For complement see A271499.

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

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

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

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

More terms from Emeric Deutsch, Aug 13 2008

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).

Original entry on oeis.org

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

Leroy Quet, Jul 22 2008

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

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

Cf. A023416, A143071, A143072.

Cf. A209229.

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

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

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

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

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

More terms from Emeric Deutsch, Aug 11 2008

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

cp's OEIS Frontend

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).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

Formula

Extensions