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

1,3

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

Example

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.

Prog

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

Crossrefs

Cf. A308251.

Sequence in context: A247063 A003726 A343110 * A004828 A032895 A032854

Adjacent sequences: A337579 A337580 A337581 * A337583 A337584 A337585

Keyword

nonn,base

Author

Rémy Sigrist, Sep 20 2020

Status

approved