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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). 5
1, 11, 1011, 10001011, 1000000010001011, 10000000000000001000000010001011, 1000000000000000000000000000000010000000000000001000000010001011, 10000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000010000000000000001000000010001011 (list; graph; refs; listen; history; text; internal format)



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).


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


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.


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

Sequence in context: A127961 A127962 A267606 * A015511 A065050 A099440

Adjacent sequences:  A303783 A303784 A303785 * A303787 A303788 A303789




Eric Angelini and Jean-Marc Falcoz, Apr 30 2018



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Last modified October 26 11:59 EDT 2021. Contains 348267 sequences. (Running on oeis4.)