A303783 Lexicographically earliest sequence of distinct terms such that what emerges from the mask is a square (see the Comment section for the mask explanation).

1, 10, 2, 11, 3, 14, 4, 19, 5, 20, 6, 21, 7, 24, 8, 29, 9, 30, 100, 12, 101, 13, 104, 15, 109, 16, 110, 17, 111, 18, 114, 22, 119, 23, 120, 25, 121, 26, 124, 27, 129, 28, 130, 31, 131, 32, 134, 33, 139, 34, 140, 35, 141, 36, 144, 37, 149, 38, 150, 39, 151, 40, 154, 41, 159, 42, 160, 43, 161, 44, 164, 45, 169, 46, 170, 47

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Apr 30 2018

Keywords

• nonn
• base

Comments

For any pair of contiguous 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 left. What is not covered by the mask forms a square number.

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 integers > 0, as all integers will appear at some point, either as mask or masked.

Examples

			In the pair (1,10), 1 is the mask; 0 emerges and is a square;
in the pair (10,2), 2 is the mask; 0 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 (11529,2018), 2018 is the mask; 9 emerges and is a square;
etc.
		

Links

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

Crossrefs

Cf. A303782 (same idea with primes), A303784 (with even numbers), A303785 (with odd numbers), A303786 (rebuilds the sequence itself term by term).