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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
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
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
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, Sep 06 2023
STATUS
approved