A083653 - OEIS

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A083653

Consider the binary Champernowne sequence (A030190): smallest number m such that in binary representation n is contained in the concatenation of m and its successors.

0, 1, 2, 1, 4, 2, 1, 3, 8, 4, 10, 2, 3, 1, 3, 7, 16, 8, 4, 9, 18, 10, 21, 2, 7, 3, 9, 1, 3, 5, 7, 15, 32, 16, 8, 17, 36, 4, 9, 19, 34, 18, 10, 10, 37, 21, 2, 6, 15, 7, 3, 12, 19, 9, 21, 1, 7, 3, 19, 5, 7, 13, 15, 31, 64, 32, 16, 33, 8, 34, 17, 35, 68, 36, 18, 4, 73, 9, 19, 39, 66, 34, 20, 18

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OFFSET

0,3

COMMENTS

a(n)<=n; see A083655 for numbers m with a(m)=m;

a(A055143(n))=1;

A083654(n)-1 = number of successors of a(n) to cover n.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, PARI program for A083653

EXAMPLE

n=24: '11000'=24 is a suffix of the concatenation of the first 8 numbers: '0'1'10'11'100'101'110'111'1000', therefore a(24)=7 and A083654(24)=2.