A366351 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared whose binary string value contains at least one binary prime factor of a(n-1).

1, 2, 4, 5, 10, 6, 3, 7, 14, 8, 9, 11, 22, 12, 13, 26, 16, 17, 34, 18, 15, 19, 38, 20, 21, 23, 46, 24, 25, 27, 28, 29, 58, 30, 31, 62, 32, 33, 35, 37, 74, 36, 39, 43, 86, 40, 41, 82, 42, 44, 45, 47, 94, 48, 49, 55, 52, 50, 51, 53, 106, 54, 56, 57, 59, 118, 60, 61, 122, 64, 65, 69, 63, 67, 134, 66

Offset

1,2

Comments

This is the base-2 equivalent of A365703. Unlike that sequence is it conjectured all numbers appear. The only fixed point in the first 10000 terms is 6, and it is likely no more exist.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Example

a(6) = 6 = 110_2 as a(5) = 10 = 2*5 = 10_2*101_2, and 6 = "110" is the smallest unused positive number to contain at least one of "10" and "101".

Crossrefs

Cf. A365703, A064413, A027748, A027746.

Sequence in context: A077389 A122991 A245512 * A378098 A232616 A125728

Adjacent sequences: A366348 A366349 A366350 * A366352 A366353 A366354

Keyword

nonn

Author

Scott R. Shannon, Oct 08 2023

Status

approved