A143070 -id:A143070 - 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

A143072 A positive integer n is included if both the number of 0's and the number of 1's in the binary representation of n are powers of 2 (including being possibly 1).

Original entry on oeis.org

2, 4, 5, 6, 9, 10, 12, 16, 23, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 135, 139, 141, 142, 147, 149, 150, 153, 154, 156, 163, 165, 166, 169, 170, 172, 177, 178, 180, 184, 195, 197, 198, 201, 202, 204, 209, 210, 212, 216, 225, 226, 228

Offset: 1

Leroy Quet, Jul 22 2008

			34 in binary is 100010. This has 4 zeros and 2 ones. And since 4 and 2 are both powers of 2, 34 is included in the sequence.

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

Cf. A023416, A000120, A143070, A143071.

Cf. A209229.

a143072 n = a143072_list !! (n-1)
a143072_list = filter ((== 1) . a209229 . a023416) a143071_list
-- Reinhard Zumkeller, Sep 14 2014

p2Q[n_]:=And@@(IntegerQ[Log[2,#]]&/@DigitCount[n,2]); Select[Range[250], p2Q] (* Harvey P. Dale, Aug 20 2013 *)

A209229(A000120(a(n))) * A209229(A023416(a(n))) = 1. - Reinhard Zumkeller, Sep 14 2014

Extended by 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).

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