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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
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
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*(w-2) + w*n) \\ Rémy Sigrist, Dec 15 2017
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Dec 14 2017
EXTENSIONS
More terms from Rémy Sigrist, Dec 15 2017
STATUS
approved