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

Author

N. J. A. Sloane, Dec 14 2017

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

PARI

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

Formula

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

Extensions

More terms from Rémy Sigrist, Dec 15 2017