A162537 a(n) is the smallest positive multiple k of n such that every length of the runs of 0's and 1's in the binary representation of k is coprime to n.

1, 2, 3, 8, 5, 42, 7, 8, 9, 10, 11, 672, 13, 14, 15, 32, 17, 522, 19, 40, 21, 682, 23, 672, 25, 130, 27, 56, 29, 2730, 31, 32, 33, 34, 35, 8352, 37, 190, 195, 40, 41, 42, 43, 2728, 45, 46, 47, 672, 49, 650, 51, 520, 53, 702, 55, 56, 171, 58, 59, 174720, 61, 62, 189, 128, 195, 8382, 67, 136, 207, 910, 71, 8352, 73, 3626, 75

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 ends by either the digit 1-b or by the end of the string.

Links

Table of n, a(n) for n=1..75.

Example

For n = 4, we check: 4 in binary is 100, which has a run of two 0's; and 2 is not coprime to 4. But 2*4 = 8 = 1000 in binary has a run of one 1 and a run of three 0's. Since both 1 and 3 are coprime to 4, a(4) = 8.

Crossrefs

Cf. A162535, A162536.

Sequence in context: A007955 A324502 A170826 * A369740 A109844 A128779

Adjacent sequences: A162534 A162535 A162536 * A162538 A162539 A162540

Keyword

base,nonn

Author

Leroy Quet, Jul 05 2009

Extensions

More terms from Sean A. Irvine, Jan 27 2011

Status

approved