A143072 - OEIS

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).

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

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OFFSET

1,1

LINKS

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

FORMULA

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

EXAMPLE

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.

MATHEMATICA

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

PROG