A362076 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-2) * a(n-1).

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

Offset: 1

Author

Scott R. Shannon, Apr 08 2023

Keywords

• nonn
• base
• fini
• full

Comments

The sequence is finite; after 6481 terms a(6480) = 5211 and a(6481) = 44444 resulting in a product of 5211 * 44444 = 231597684. This contains all digits 1 to 9 so the next term does not exist.

The sequence contains 40 fixed points, the last being a(5477).

Examples

			a(12) = 22 as a(10) * a(11) = 10 * 11 = 110, and 22 is the smallest unused number that does not contain the digits 0 or 1.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..6481
• Michael S. Branicky, Python program
• Scott R. Shannon, Image of the 6481 terms. The green line is a(n) = n.

Crossrefs

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

Programs

Python

# see linked program