

A296354


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


5



0, 1, 6, 8, 22, 25, 28, 31, 66, 70, 74, 78, 82, 86, 90, 94, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 450, 456, 462, 468, 474, 480, 486, 492, 498, 504, 510, 516, 522, 528, 534, 540, 546, 552, 558, 564, 570, 576, 582, 588
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OFFSET

0,3


COMMENTS

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.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..16384


FORMULA

a(n) = A036799(A029837(n + 1)  1) + A029837(n + 1) * n.  Rémy Sigrist, Dec 15 2017


EXAMPLE

Here is the list A076478 broken up to show the successive binary numbers (the indexing starts at 0):
0,
1,
0,0,
0,1,
1,0,
1,1,
0,0,0,
0,0,1,
0,1,0,
0,1,1,
1,0,0,
1,0,1,
...
2 = 1,0 starts at position 6, so a(2) = 6.
4 = 1,0,0 starts at position 22, so a(4) = 22.


PROG

(PARI) a(n) = my (w=#binary(n)); return (2 + 2^w*(w2) + w*n) \\ Rémy Sigrist, Dec 15 2017


CROSSREFS

Cf. A029837, A036799, A061168, A076478, A296355, A296356.
Sequence in context: A242504 A267023 A084962 * A343759 A024306 A024868
Adjacent sequences: A296351 A296352 A296353 * A296355 A296356 A296357


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, Dec 14 2017


EXTENSIONS

More terms from Rémy Sigrist, Dec 15 2017


STATUS

approved



