A369303 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused number whose string value contains the comma transform (cf. A367360) of the previous two terms.

1, 2, 12, 21, 22, 112, 121, 210, 120, 10, 11, 13, 110, 31, 3, 113, 131, 231, 122, 111, 211, 123, 114, 310, 43, 4, 34, 143, 41, 134, 115, 141, 51, 15, 116, 151, 61, 16, 117, 161, 71, 17, 118, 171, 81, 18, 119, 181, 91, 19, 311, 93, 190, 312, 23, 220, 32, 30, 223, 20, 132, 14, 212, 42, 24, 221

Offset

1,2

Comments

The sequence is conjectured to be a permutation of the positive integers. The fixed points begin 1, 2, 10, 11, 2863, 3164, 3545, 3947, 6835, 6947, 7052, ... although it is likely there are infinitely more.

Links

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

Scott R. Shannon, Image of the first one million terms. The green line is a(n) = n.

Example

a(3) = 12 as the comma transform of 1 and 2 is 12.
a(6) = 112 as the comma transform of 21 and 22 is 12, but 12 has already appeared so the next lowest unused number to contain '12' is 112.

Crossrefs

Cf. A367360, A121805, A367362.

Sequence in context: A096108 A098941 A231875 * A031001 A048955 A034049

Adjacent sequences: A369300 A369301 A369302 * A369304 A369305 A369306

Keyword

nonn,base,look

Author

Scott R. Shannon, Jan 19 2024

Status

approved