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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.

%I A083653 #11 Jun 24 2021 13:42:59
%S A083653 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,
%T A083653 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,
%U A083653 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
%N 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.
%C A083653 a(n)<=n; see A083655 for numbers m with a(m)=m;
%C A083653 a(A055143(n))=1;
%C A083653 A083654(n)-1 = number of successors of a(n) to cover n.
%H A083653 Rémy Sigrist, <a href="/A083653/b083653.txt">Table of n, a(n) for n = 0..8191</a>
%H A083653 Rémy Sigrist, <a href="/A083653/a083653.gp.txt">PARI program for A083653</a>
%e A083653 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.
%o A083653 (PARI) See Links section.
%Y A083653 Cf. A030190, A030304, A007088, A345672 (decimal analog).
%Y A083653 Cf. A055143, A083654, A083655.
%K A083653 nonn,base
%O A083653 0,3
%A A083653 _Reinhard Zumkeller_, May 01 2003
%E A083653 Edited by _Charles R Greathouse IV_, Apr 26 2010