A303786 Lexicographically earliest sequence of distinct terms such that what emerges from the mask rebuilds the sequence itself, term by term (see the Comment section for the mask explanation).

1, 11, 1011, 10001011, 1000000010001011, 10000000000000001000000010001011, 1000000000000000000000000000000010000000000000001000000010001011, 10000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000010000000000000001000000010001011

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 rebuilds, term by term, the starting sequence.

The n-th term of the sequence has exactly 2^(n-1) digits, which means that a(21) has more than one million digits.

The sequence starts with a(1) = 1, then a(n) = 10^(2^(n-1)-1)+a(n-1).

Examples

			In the pair (1,11), 1 is the mask; 1 emerges = a(1);
In the pair (11,1011), 11 is the mask; 11 emerges = a(2);
In the pair (1011,10001011), 1011 is the mask; 1011 emerges = a(3); etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..11

Crossrefs

Cf. A303782 (same idea with primes), A303783 (with squares), A303784 (with even numbers), A303785 (with odd numbers).