A338265 If a(n) has at least one common digit with a(n-1), underline a(n). The non-underlined terms reproduce the sequence itself.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 20, 11, 31, 23, 22, 24, 25, 26, 27, 28, 29, 32, 30, 12, 41, 34, 33, 35, 36, 37, 38, 39, 43, 40, 13, 51, 45, 42, 44, 46, 47, 48, 49, 54, 50, 14, 61, 56, 52, 53, 55, 57, 58, 59, 65, 60, 15, 71, 67, 62, 63, 64, 66, 68, 69, 76, 70, 16, 81, 78, 72

Offset: 1

Author

Eric Angelini, Oct 19 2020

Keywords

• base
• nonn

Comments

This is a kind of fractal sequence as it contains an infinite number of copies of itself. The underlined terms of the sequence are the lexicographically earliest permutation of the natural numbers > 10.

Examples

			If we erase the parenthesized terms, we get the sequence itself: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, (11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 20), 11, (31, 23, 22, 24, 25, 26, 27, 28, 29, 32, 30), 12, (41, 34, 33, 35, 36, 37, 38, 39, 43, 40), 13, (51, 45, 42, 44, 46, 47, 48, 49, 54, 50), 14, (61, 56, 52, 53, 55, 57, 58, 59, 65, 60), 15, (71, 67, 62, 63, 64, 66, 68, 69, 76, 70), 16, (81, 78, 72, ...) etc.
		

Crossrefs

Cf. A274329.