A303848 Lexicographically earliest sequence of distinct terms such that what emerges from the mask (right-aligned) is a square (see the Comments section for the mask explanation).

1, 10, 2, 11, 3, 12, 4, 13, 5, 14, 6, 15, 7, 16, 8, 17, 9, 18, 100, 19, 101, 20, 102, 21, 103, 22, 104, 23, 105, 24, 106, 25, 107, 26, 108, 27, 109, 28, 110, 29, 111, 30, 112, 31, 113, 32, 114, 33, 115, 34, 116, 35, 117, 36, 118, 37, 119, 38, 120, 39, 121, 40, 122, 41, 123, 42, 124, 43, 125, 44, 126, 45, 127, 46, 128, 47

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, May 01 2018

Keywords

• nonn
• base

Comments

For any pair of consecutive terms, one of the terms uses fewer digits than the other. This term is called the mask. Put the mask on the other term, starting from the right. What is not covered by the mask forms a square number on the left.

The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.

This sequence is a permutation of the positive integers, as all integers will appear at some point, either as mask or masked.

Isn't "what emerges" always a 1, and two adjacent terms are always of the form (xxx, 1yyy) or (1yyy, xxx) where xxx is the least unused n-digit number and 1yyy is the least unused (n+1)-digit number? - M. F. Hasler, May 30 2023

Examples

			In the pair (1,10), 1 is the mask; 1 emerges and is a square;
in the pair (10,2), 2 is the mask; 1 emerges and is a square;
in the pair (2,11), 2 is the mask; 1 emerges and is a square;
in the pair (11,3), 3 is the mask; 1 emerges and is a square;
...
in the pair (10199,2018), 2018 is the mask; 1 emerges and is a square;
etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A303783 (same idea, but the mask is left-aligned).