A296355 - OEIS

%I #25 Dec 20 2017 13:05:59

%S 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 20,27,63,174,9,111,51,1,41,22,70,17,49,15,74,55,6,154,25,78,8,65,21,

%U 59,48,73,5,28,31,20,135,27,63,89,174,445,33,9,120,111,66

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

%C 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 In fact every number > 1 appears earlier - see A296356 for the proof.

%H Rémy Sigrist, <a href="/A296355/b296355.txt">Table of n, a(n) for n = 0..16384</a>

%H Rémy Sigrist, <a href="/A296355/a296355.pl.txt">Perl program for A296355</a>

%e Here is the list A076478 broken up to show the successive binary numbers (the indexing starts at 0):

%e 0,

%e 1,

%e 0,0,

%e 0,1,

%e 1,0,

%e 1,1,

%e 0,0,0,

%e 0,0,1,

%e 0,1,0,

%e 0,1,1,

%e 1,0,0,

%e 1,0,1,

%e ...

%e 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 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 Cf. A076478, A061168. A296354, A296356.

%K nonn,base,look

%O 0,4

%A _N. J. A. Sloane_, Dec 14 2017; corrected and extended Dec 17 2017

%E More terms from _Rémy Sigrist_, Dec 19 2017