A162534 A positive integer k is included if every length of the runs of 0's and 1's in the binary representation of k divides k.

1, 2, 4, 5, 6, 10, 12, 16, 18, 20, 21, 22, 24, 26, 36, 38, 42, 44, 48, 50, 52, 54, 60, 65, 69, 72, 74, 76, 78, 80, 81, 82, 84, 85, 86, 87, 90, 93, 95, 100, 102, 106, 108, 114, 117, 120, 125, 126, 130, 132, 138, 144, 146, 148, 150, 154, 156, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 186, 188, 190, 192, 198

Offset

1,2

Comments

By "run" of 0's or 1's, it is meant: Think of binary k as a string of 0's and 1's. A single run of the digit b (0 or 1) is made up completely of consecutive digits all equal to b, and is bounded on its end by either the digit 1-b or the end of the string.

Links

Table of n, a(n) for n=1..74.

Example

198 in binary is 11000110. There are two runs of two 1's each in this representation, and a run of three 0's and a run of one 0. Since 198 is divisible by each of these lengths (1,2, and 3), 198 is in the sequence.

Crossrefs

Cf. A162535, A162536.

Sequence in context: A233413 A128167 A364214 * A233193 A177911 A127092

Adjacent sequences: A162531 A162532 A162533 * A162535 A162536 A162537

Keyword

base,nonn

Author

Leroy Quet, Jul 05 2009

Extensions

More terms from Sean A. Irvine, Jan 26 2011

Status

approved