cp's OEIS Frontend

A296354 Official position where binary expansion of n starts in the list of binary numbers in the binary Champernowne sequence A076478.

%I A296354 #20 Dec 17 2017 21:43:01
%S A296354 0,1,6,8,22,25,28,31,66,70,74,78,82,86,90,94,178,183,188,193,198,203,
%T A296354 208,213,218,223,228,233,238,243,248,253,450,456,462,468,474,480,486,
%U A296354 492,498,504,510,516,522,528,534,540,546,552,558,564,570,576,582,588
%N A296354 Official position where binary expansion of n starts in the list of binary numbers in the binary Champernowne sequence A076478.
%C A296354 a(n) is the official position where the binary expansion of n appears. The binary expansion of n may also appear earlier, by accident, see A296355 and A296356.
%H A296354 Rémy Sigrist, <a href="/A296354/b296354.txt">Table of n, a(n) for n = 0..16384</a>
%F A296354 a(n) = A036799(A029837(n + 1) - 1) + A029837(n + 1) * n. - _Rémy Sigrist_, Dec 15 2017
%e A296354 Here is the list A076478 broken up to show the successive binary numbers (the indexing starts at 0):
%e A296354 0,
%e A296354 1,
%e A296354 0,0,
%e A296354 0,1,
%e A296354 1,0,
%e A296354 1,1,
%e A296354 0,0,0,
%e A296354 0,0,1,
%e A296354 0,1,0,
%e A296354 0,1,1,
%e A296354 1,0,0,
%e A296354 1,0,1,
%e A296354 ...
%e A296354 2 = 1,0 starts at position 6, so a(2) = 6.
%e A296354 4 = 1,0,0 starts at position 22, so a(4) = 22.
%o A296354 (PARI) a(n) = my (w=#binary(n)); return (2 + 2^w*(w-2) + w*n) \\ _Rémy Sigrist_, Dec 15 2017
%Y A296354 Cf. A029837, A036799, A061168, A076478, A296355, A296356.
%K A296354 nonn,base
%O A296354 0,3
%A A296354 _N. J. A. Sloane_, Dec 14 2017
%E A296354 More terms from _Rémy Sigrist_, Dec 15 2017