A337582 Numbers m such that m AND (m*2^k) is zero or a power of 2 for any k > 0 (where AND denotes the bitwise AND operator).

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 22, 24, 25, 26, 32, 33, 34, 35, 36, 37, 38, 40, 41, 44, 48, 49, 50, 52, 64, 65, 66, 67, 68, 69, 70, 72, 74, 76, 80, 81, 82, 83, 88, 96, 97, 98, 100, 101, 104, 128, 129, 130, 131, 132, 133, 134, 136

Offset: 1

Author

Rémy Sigrist, Sep 20 2020

Keywords

• nonn
• base

Comments

For any k > 0, there are A308251(k-1) positive terms with k binary digits.

The ones in the binary representation of any term encodes a finite set of nonnegative integers, say S, such that the differences between any two distinct elements of S are all unique.

For any m >= 0, m belongs to the sequence iff 2*m belongs to the sequence.

Examples

			Regarding 7:
- 7 AND 14 = 6, which is neither 0 nor a power of 2,
- so 7 does not belong to the sequence.
Regarding 13:
- we have the following values:
    k    13 AND (13*2^k)
    ---  ---------------
      1              2^3
      2              2^2
      3              2^3
    >=4                0
- so 13 belongs to the sequence.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A308251.

Programs

PARI

is(n) = { my (m=n); while (m>>=1, if (hammingweight(bitand(m,n))>1, return (0))); return (1) }