A367646 a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-1) - GCT(a(n-2),a(n-1)) if nonnegative and not already in the sequence, else a(n) = a(n-1) + CT(a(n-2),a(n-1)), where CT(a,b) is the Comma transform (cf. A367360) of a and b, while GCT(a,b) is the largest possible generalized Command transform (cf. A367635) where at least one digit of both a and b can be chosen.

0, 1, 2, 14, 35, 78, 21, 103, 92, 53, 28, 60, 146, 132, 71, 44, 30, 73, 66, 102, 41, 17, 6, 82, 150, 129, 117, 26, 98, 29, 111, 20, 8, 16, 97, 166, 95, 164, 113, 72, 109, 88, 186, 105, 166, 115, 54, 109, 68, 164, 83, 131, 100, 89, 81, 179, 62, 158, 137, 56, 131, 70, 87, 79, 156, 65, 131, 80

Offset

0,3

Comments

This is a variation of A367578, where one can choose more than one digit from both a(n-2) and a(n-1) to create the largest possible step to a nonnegative number which has not previously appeared to form a(n). If all such numbers have already appeared the smallest possible forward step is chosen, which is just the standard Comma transform of a(n-2) and a(n-1).

It is conjectured that all nonnegative numbers appear in the sequence. After the first 10 million terms the only fixed points are 0, 1, 2, 29, 65, 84, 222, 377, 491, 499, and it is likely no more exist. The first number to appear twice is a(35) = a(44) = 166.

Links

Scott R. Shannon, Table of n, a(n) for n = 0..10000

Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Scott R. Shannon, Image of the first 10 million terms.

Example

a(3) = 14 as CT(a(1),a(2)) = CT(1,2) = 12, so a(3) = a(2) + 12 = 14.
a(6) = 21 as GCT(a(4),a(5)) = GCT(35,78) = 57, so a(6) = a(5) - 57 = 21, as 21 is nonnegative and not already in the sequence.
a(13) = 132 as GCT(a(11),a(12)) = GCT(60,146) = 14, so a(13) = a(12) - 14 = 132, as 132 is nonnegative and not already in the sequence. This is the first term to differ from A367578.

Crossrefs

Cf. A367360, A367635, A367578, A005132, A121805.

Sequence in context: A291152 A145910 A128126 * A367578 A134647 A004117

Adjacent sequences: A367643 A367644 A367645 * A367647 A367648 A367649

Keyword

nonn,base

Author

Scott R. Shannon, Nov 25 2023

Status

approved