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, 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.

Links

Table of n, a(n) for n=1..48.

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

Cf. A365703, A064413, A027748, A027746.

Sequence in context: A009514 A192851 A112718 * A117301 A141079 A269841

Adjacent sequences: A365497 A365498 A365499 * A365501 A365502 A365503

Keyword

nonn,base

Author

Scott R. Shannon, Sep 06 2023

Status

approved