A175415 Those positive integers n that when written in binary, each run of 0's and 1's has a length which divides the number of binary digits of n.

1, 2, 3, 5, 7, 9, 10, 11, 12, 13, 15, 21, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 63, 85, 127, 132, 133, 134, 144, 146, 147, 148, 149, 150, 153, 154, 155, 158, 161, 164, 165, 166, 169, 170, 171, 172

Offset

1,2

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Example

35 in binary is 100011. There is a run of one 1, followed by a run of three 0's, followed finally by a run of two 1's. And there are six binary digits all together. Since 1, 3, and 2 each divide 6, then 35 is in the sequence.

Prog

(Python)
from itertools import groupby
def ok(n):
    b = bin(n)[2:]
    return all(len(b)%len(list(g)) == 0 for k, g in groupby(b))
print([k for k in range(1, 173) if ok(k)]) # Michael S. Branicky, Nov 07 2022

Crossrefs

Cf. A175416

Sequence in context: A089743 A080587 A342190 * A304721 A063464 A341518

Adjacent sequences: A175412 A175413 A175414 * A175416 A175417 A175418

Keyword

base,nonn

Author

Leroy Quet, May 07 2010

Status

approved