A368559 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that a(n) contains all the distinct digits of a(n-1) - a(n-2).

1, 2, 10, 8, 12, 4, 18, 14, 24, 100, 67, 3, 46, 34, 21, 13, 28, 15, 31, 16, 51, 35, 61, 26, 53, 27, 62, 135, 37, 89, 25, 64, 39, 52, 103, 105, 20, 58, 38, 102, 146, 40, 106, 6, 101, 59, 42, 17, 125, 108, 71, 73, 22, 115, 93, 23, 70, 47, 32, 145, 113, 123, 104, 19, 85, 36, 49, 130, 81, 94

Offset: 1

Author

Scott R. Shannon, Dec 30 2023

Keywords

• nonn
• base

Comments

The sequence is conjectured to be a permutation of the positive integers. The fixed points begin 1, 2, 95, 122, 156, 318, 1644, 1964, 2189, 2740, 8264, 16904, ... although it is likely there are infinitely more.

Examples

			a(3) = 10 as a(2) - a(1) = 2 - 1 = 1, and 10 is the smallest unused number to contain 1.
a(11) = 67 as a(10) - a(9) = 100 - 24 = 76, and 67 is the smallest unused number to contain 7 and 6.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Scott R. Shannon, Image of the first 250000 terms. The green line is a(n) = n.

Crossrefs

Cf. A362093, A362075, A184992, A069638.