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

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

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*(w-2) + w*n) \\ Rémy Sigrist, Dec 15 2017

Crossrefs

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

Sequence in context: A267023 A084962 A365649 * 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