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A365500
a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared whose string value contains all the distinct prime factors of a(n-1). Overlapping factor strings is allowed.
1
1, 2, 12, 23, 123, 341, 311, 1311, 1923, 3641, 3311, 11437, 111437, 237147, 137577, 11379, 3793, 13793, 10613, 106130, 1061325, 5389, 317, 1317, 439, 1439, 11439, 3141, 349, 1349, 719, 1719, 1913, 11913, 1193, 11193, 4137, 1973, 11973, 1307, 11307, 3769, 13769, 2817, 313, 1313, 1013, 10130
OFFSET
1,2
COMMENTS
Any number that contains only nonprime digits, does not contain any substring that is prime, and is not itself a prime can never appear, e.g., 4, 6, 8, 9, 10, 14.
FORMULA
a(3) = 12 as a(2) = 2 and "12" is the smallest unused number to contain "2".
a(4) = 23 as a(3) = 12 = 2*2*3 and "23" is the smallest unused number to contain both "2" and "3".
a(7) = 311 as a(6) = 341 = 11*31 and "311" is the smallest unused number to contain both "11" and "31". This is the first term to contain overlapping factor strings.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, Sep 06 2023
STATUS
approved