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 1-4 of 4 results.

A143579 Permutation of the natural numbers (0,1,2,3,...): Odious numbers (A000069) interleaved with Evil numbers (A001969).

Original entry on oeis.org

1, 0, 2, 3, 4, 5, 7, 6, 8, 9, 11, 10, 13, 12, 14, 15, 16, 17, 19, 18, 21, 20, 22, 23, 25, 24, 26, 27, 28, 29, 31, 30, 32, 33, 35, 34, 37, 36, 38, 39, 41, 40, 42, 43, 44, 45, 47, 46, 49, 48, 50, 51, 52, 53, 55, 54, 56, 57, 59, 58, 61, 60, 62, 63, 64, 65, 67, 66, 69, 68, 70, 71, 73
Offset: 0

Views

Author

Gary W. Adamson, Aug 24 2008

Keywords

Comments

This is the lodumo_2 of the Thue-Morse sequence A010059, where lodumo_k of sequences is defined in A159970. [Philippe Deléham, Apr 29 2009]

Crossrefs

Cf. A000069, A001969, A160017.

Formula

Antidiagonals of an array, Odious numbers (A000069) in row 1 and Evil numbers (A001969) in row 2: 1, 2, 4, 7, 8, 11, 13,... 0, 3, 5, 6, 9, 10, 12,...

Extensions

Extended by R. J. Mathar, Sep 05 2008
Edited by R. J. Mathar, Feb 04 2010

A160017 Lodumo_2 of Thue-Morse sequence A010060.

Original entry on oeis.org

0, 1, 3, 2, 5, 4, 6, 7, 9, 8, 10, 11, 12, 13, 15, 14, 17, 16, 18, 19, 20, 21, 23, 22, 24, 25, 27, 26, 29, 28, 30, 31, 33, 32, 34, 35, 36, 37, 39, 38, 40, 41, 43, 42, 45, 44, 46, 47, 48, 49, 51, 50, 53, 52, 54, 55, 57, 56, 58, 59, 60, 61, 63, 62, 65, 64, 66, 67, 68, 69, 71, 70, 72
Offset: 0

Views

Author

Philippe Deléham, Apr 29 2009

Keywords

Comments

Permutation of nonnegative integers .
Evil numbers (A001969) interleaved with Odious numbers (A000069). - Philippe Deléham, Jan 01 2012

Crossrefs

Cf. A010060, A143579, A159970 (for definition of lodumo_k of sequences).

Programs

Formula

a(n)=lod_2(A010060(n)).

Extensions

Corrected by R. J. Mathar, May 02 2009

A203553 Lodumo_2 of A118175, which is n 1's followed by n 0's.

Original entry on oeis.org

1, 0, 3, 5, 2, 4, 7, 9, 11, 6, 8, 10, 13, 15, 17, 19, 12, 14, 16, 18, 21, 23, 25, 27, 29, 20, 22, 24, 26, 28, 31, 33, 35, 37, 39, 41, 30, 32, 34, 36, 38, 40, 43, 45, 47, 49, 51, 53, 55, 42, 44, 46, 48, 50, 52, 54, 57, 59, 61, 63, 65, 67, 69, 71, 56, 58, 60, 62, 64, 66, 68, 70
Offset: 0

Views

Author

Philippe Deléham, Jan 02 2012

Keywords

Comments

Permutation of nonnegative numbers.
Lodumo_k of sequences is defined in A159970.
The sequence has a natural decomposition into irregular triangle (see example). The length of row n is A008619 (n). Row sums are the cubes (A000578) interspersed with A007531.

Examples

			Triangle begins :
1
0
3, 5
2, 4
7, 9, 11
6, 8, 10
13, 15, 17, 19
12, 14, 16, 18
21, 23, 25, 27, 29
20, 22, 24, 26, 28
31, 33, 35, 37, 39, 41
30, 32, 34, 36, 38, 40
43, 45, 47, 49, 51, 53, 55
42, 44, 46, 48, 50, 52, 54
57, 59, 61, 63, 65, 67, 69, 71
56, 58, 60, 62, 64, 66, 68, 70
73, 75, 77, 79, 81, 83, 85, 87, 89
72, 74, 76, 78, 80, 82, 84, 86, 88 ...
Row sums : 1 = 1^3 ; 0 = 1^3 - 1 ; 3 + 5 = 2^3 ; 2 + 4 = 2^3 - 2 = 6 ; 7 + 9 + 11 = 3^3 = 27 ; 6 + 8 + 10 = 3^3 - 3 = 24 ; 13 + 15 + 17 + 19 = 4^3 = 64 ; 12 + 14 + 16 + 18 = 4^4 - 4 = 60 ; ...

Crossrefs

Cf. A118175, A159970, A203554.
Cf. A000578, A007531, A002061, A002378, A028387, A028552.

Formula

a(n)= Lodumo_2(A118175(n)).

A203554 Lodumo_2 of A079813, which is n 0's followed by n 1's.

Original entry on oeis.org

0, 1, 2, 4, 3, 5, 6, 8, 10, 7, 9, 11, 12, 14, 16, 18, 13, 15, 17, 19, 20, 22, 24, 26, 28, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 40, 31, 33, 35, 37, 39, 41, 42, 44, 46, 48, 50, 52, 54, 43, 45, 47, 49, 51, 53, 55
Offset: 0

Views

Author

Philippe Deléham, Jan 02 2012

Keywords

Comments

Permutation of nonnegative numbers.
Lodumo_k of sequences is defined in A159970.
The sequence has a natural decomposition into irregular triangle (see example). The length of row n is A008619(n). Rows sums are the cubes (A000578) interspersed with A007531. First column: A002378 interspersed with A002061.

Examples

			Triangle begins :
0
1
2, 4
3, 5
6, 8, 10
7, 9, 11
12, 14, 16, 18
13, 15, 17, 19
20, 22, 24, 26, 28
21, 23, 25, 27, 29
30, 32, 34, 36, 38, 40
31, 33, 35, 37, 39, 41
42, 44, 46, 48, 50, 52, 54
43, 45, 47, 49, 51, 53, 55
56, 58, 60, 62, 64, 66, 68, 70
57, 59, 61, 63, 65, 67, 69, 71
72, 74, 76, 78, 80, 82, 84, 86, 88
73, 75, 77, 79, 81, 83, 85, 87, 89...
Row sums : 0 = 1^3 -1 = 0 ; 1 = 1^3 = 1 ; 2 + 4 = 2^3 - 2 = 6 ; 3 + 5 = 2^3 = 8 ; 6 + 8 + 10 = 3^3 - 3 = 24 ; 7 + 9 + 11 = 3^3 = 27 ; 12 + 14 + 16 + 18 = 4^3 - 4 = 60 ; 13 + 15 + 17 + 19 = 4^3 = 64 ; 20 + 22 + 24 + 26 + 28 = 5^3 - 5 = 120 ; 21 + 23 + 25 + 27 + 29 = 5^3 = 125 ; etc...

Crossrefs

Cf. A079813, A159970, A203553.
Cf. A028387, A028552, A002061, A002378, A000578, A007531.
Showing 1-4 of 4 results.

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