A296354 - OEIS

%I #20 Dec 17 2017 21:43:01

%S 0,1,6,8,22,25,28,31,66,70,74,78,82,86,90,94,178,183,188,193,198,203,

%T 208,213,218,223,228,233,238,243,248,253,450,456,462,468,474,480,486,

%U 492,498,504,510,516,522,528,534,540,546,552,558,564,570,576,582,588

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

%C 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 Rémy Sigrist, <a href="/A296354/b296354.txt">Table of n, a(n) for n = 0..16384</a>

%F a(n) = A036799(A029837(n + 1) - 1) + A029837(n + 1) * n. - _Rémy Sigrist_, Dec 15 2017

%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 starts at position 6, so a(2) = 6.

%e 4 = 1,0,0 starts at position 22, so a(4) = 22.

%o (PARI) a(n) = my (w=#binary(n)); return (2 + 2^w*(w-2) + w*n) \\ _Rémy Sigrist_, Dec 15 2017

%Y Cf. A029837, A036799, A061168, A076478, A296355, A296356.

%K nonn,base

%O 0,3

%A _N. J. A. Sloane_, Dec 14 2017

%E More terms from _Rémy Sigrist_, Dec 15 2017