cp's OEIS Frontend

A296355 True position where binary expansion of n starts in the list of binary numbers in the binary Champernowne sequence A076478.

%I A296355 #25 Dec 20 2017 13:05:59
%S A296355 0,1,1,5,1,6,5,20,1,17,15,6,8,5,20,63,9,1,22,17,15,55,6,25,8,21,48,5,
%T A296355 20,27,63,174,9,111,51,1,41,22,70,17,49,15,74,55,6,154,25,78,8,65,21,
%U A296355 59,48,73,5,28,31,20,135,27,63,89,174,445,33,9,120,111,66
%N A296355 True position where binary expansion of n starts in the list of binary numbers in the binary Champernowne sequence A076478.
%C A296355 A296354(n) is the official position where the binary expansion of n appears in A076478, but the binary expansion of n may also appear earlier, by accident, and it is that starting position that is listed here.
%C A296355 In fact every number > 1 appears earlier - see A296356 for the proof.
%H A296355 Rémy Sigrist, <a href="/A296355/b296355.txt">Table of n, a(n) for n = 0..16384</a>
%H A296355 Rémy Sigrist, <a href="/A296355/a296355.pl.txt">Perl program for A296355</a>
%e A296355 Here is the list A076478 broken up to show the successive binary numbers (the indexing starts at 0):
%e A296355 0,
%e A296355 1,
%e A296355 0,0,
%e A296355 0,1,
%e A296355 1,0,
%e A296355 1,1,
%e A296355 0,0,0,
%e A296355 0,0,1,
%e A296355 0,1,0,
%e A296355 0,1,1,
%e A296355 1,0,0,
%e A296355 1,0,1,
%e A296355 ...
%e A296355 2 = 1,0 officially starts at position 6, so A076478(2) = 6, but 1,0 actually can be seen starting at position 1, so a(2) = 1.
%e A296355 4 = 1,0,0 officially starts at position 22, so A076478(4) = 22, but 1,0,0 actually can be seen starting at position 1, so a(4) = 1.
%Y A296355 Cf. A076478, A061168. A296354, A296356.
%K A296355 nonn,base,look
%O A296355 0,4
%A A296355 _N. J. A. Sloane_, Dec 14 2017; corrected and extended Dec 17 2017
%E A296355 More terms from _Rémy Sigrist_, Dec 19 2017