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

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A030190, A030304, A007088, A345672 (decimal analog).

Cf. A055143, A083654, A083655.

Sequence in context: A118235 A346702 A304624 * A278290 A135152 A329504

Adjacent sequences: A083650 A083651 A083652 * A083654 A083655 A083656

Keyword

nonn,base

Author

Reinhard Zumkeller, May 01 2003

Extensions

Edited by Charles R Greathouse IV, Apr 26 2010

Status

approved