A362093 a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-1) - a(n-2).

1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 22, 10, 30, 11, 23, 33, 24, 12, 34, 13, 35, 14, 36, 15, 37, 16, 38, 17, 39, 18, 40, 19, 43, 31, 44, 25, 26, 27, 28, 29, 32, 21, 42, 45, 41, 50, 46, 51, 47, 52, 48, 53, 49, 55, 54, 56, 57, 58, 59, 60, 62, 61, 63, 64, 65, 66, 67, 68, 69, 70, 72, 71, 73, 74, 75, 76, 77

Offset: 1

Author

Scott R. Shannon, Apr 08 2023

Keywords

• nonn

Comments

The sequence is likely to be finite although it contains at least 1 million terms.

Sequence is finite with 6080472 terms, since a(6080471) = 660606060 and a(6080472) = 8822811 have difference -651783249. - Michael S. Branicky, Apr 09 2023

Examples

			a(11) = 22 as a(10) - a(9) = 20 - 9 = 11, and 22 is the smallest unused number that does not contain the digit 1.
		

Links

• Michael S. Branicky, Python program
• Scott R. Shannon, Image of the first 1 million terms. The green line is a(n) = n.

Crossrefs

Cf. A362075, A362076, A342441, A342442, A067581, A297065.

Programs

Python

# see link for program that generates full sequence