A365501 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 all the binary distinct prime factors of a(n-1). Overlapping factor strings is allowed.

1, 2, 4, 5, 10, 11, 22, 23, 46, 47, 94, 95, 77, 55, 27, 3, 6, 12, 13, 26, 29, 58, 59, 118, 119, 71, 142, 143, 45, 43, 86, 87, 61, 122, 123, 83, 166, 167, 334, 335, 269, 538, 539, 92, 93, 31, 62, 124, 125, 20, 21, 7, 14, 28, 30, 44, 54, 19, 38, 39, 52, 53, 106, 107, 214, 215, 171, 51, 35, 110, 75

Offset

1,2

Comments

This is the base-2 equivalent of A365500. As the term a(3) = 4 is not immediately followed by 8, 8 and other higher powers of 2 will never appear as they could only be the following term of a smaller power of 2.

In the first 10000 terms the fixed points are 239, 373, 488, 854, 942, 3573, 5580, 5968.

Links

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

Example

a(6) = 11 = 1011_2 as a(5) = 10 which contains 2 = 10_2 and 5 = 101_2 as distinct prime factors, and the string "1011" contains both "10" and "101" as substrings.

Crossrefs

Cf. A365500, A365703, A027748, A064413.

Sequence in context: A328009 A128216 A299322 * A080735 A091856 A083416

Adjacent sequences: A365498 A365499 A365500 * A365502 A365503 A365504

Keyword

nonn,base

Author

Scott R. Shannon, Sep 06 2023

Status

approved