cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Dec 14 2017

Keywords

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

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

A296355 True position where binary expansion of n starts in the list of binary numbers in the binary Champernowne sequence A076478.

Original entry on oeis.org

0, 1, 1, 5, 1, 6, 5, 20, 1, 17, 15, 6, 8, 5, 20, 63, 9, 1, 22, 17, 15, 55, 6, 25, 8, 21, 48, 5, 20, 27, 63, 174, 9, 111, 51, 1, 41, 22, 70, 17, 49, 15, 74, 55, 6, 154, 25, 78, 8, 65, 21, 59, 48, 73, 5, 28, 31, 20, 135, 27, 63, 89, 174, 445, 33, 9, 120, 111, 66
Offset: 0

Views

Author

N. J. A. Sloane, Dec 14 2017; corrected and extended Dec 17 2017

Keywords

Comments

A296354(n) is the official position where the binary expansion of n appears in A076478, but the binary expansion of n may also appear earlier, by accident, and it is that starting position that is listed here.
In fact every number > 1 appears earlier - see A296356 for the proof.

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 officially starts at position 6, so A076478(2) = 6, but 1,0 actually can be seen starting at position 1, so a(2) = 1.
4 = 1,0,0 officially starts at position 22, so A076478(4) = 22, but 1,0,0 actually can be seen starting at position 1, so a(4) = 1.

Links

Crossrefs

Cf. A076478, A061168. A296354, A296356.

Extensions

More terms from Rémy Sigrist, Dec 19 2017

A296364 a(n) = A296349(n) - A030304(n).

Original entry on oeis.org

0, 0, 0, 3, 0, 7, 11, 11, 0, 16, 0, 28, 29, 37, 38, 31, 0, 37, 54, 43, 7, 49, 3, 83, 73, 90, 75, 104, 106, 104, 105, 79, 0, 86, 124, 93, 0, 154, 144, 107, 32, 121, 164, 168, 39, 131, 212, 207, 177, 215, 233, 210, 181, 231, 183, 267, 258, 276, 218, 281
Offset: 0

Views

Author

N. J. A. Sloane, Dec 16 2017

Keywords

Comments

Another measure of the binary "early-birdness" of n (cf. A296356, A116700).

Crossrefs

Cf. A296349, A030304, A116700, A296356.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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