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.

A256997 Square array A(row,col) read by antidiagonals: A(1,col) = A055938(col), and for row > 1, A(row,col) = A005187(A(row-1,col)).

Original entry on oeis.org

2, 5, 3, 6, 8, 4, 9, 10, 15, 7, 12, 16, 18, 26, 11, 13, 22, 31, 34, 49, 19, 14, 23, 41, 57, 66, 95, 35, 17, 25, 42, 79, 110, 130, 184, 67, 20, 32, 47, 81, 153, 215, 258, 364, 131, 21, 38, 63, 89, 159, 302, 424, 514, 723, 259, 24, 39, 73, 120, 174, 312, 599, 844, 1026, 1440, 515, 27, 46, 74, 143, 236, 343, 620, 1192, 1683, 2050, 2876, 1027
Offset: 2

Views

Author

Antti Karttunen, Apr 14 2015

Keywords

Comments

The array is read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
This is transpose of array A256995.
If we assume that a(1) = 1 (but which is not explicitly included here because outside of the array proper), then A256998 gives the inverse permutation.

Examples

			The top left corner of the array:
    2,    5,    6,    9,   12,   13,   14,   17,   20,   21,    24,    27
    3,    8,   10,   16,   22,   23,   25,   32,   38,   39,    46,    50
    4,   15,   18,   31,   41,   42,   47,   63,   73,   74,    88,    97
    7,   26,   34,   57,   79,   81,   89,  120,  143,  145,   173,   191
   11,   49,   66,  110,  153,  159,  174,  236,  281,  287,   341,   375
   19,   95,  130,  215,  302,  312,  343,  467,  558,  568,   677,   743
   35,  184,  258,  424,  599,  620,  680,  928, 1111, 1132,  1349,  1479
   67,  364,  514,  844, 1192, 1235, 1356, 1852, 2216, 2259,  2693,  2951
  131,  723, 1026, 1683, 2380, 2464, 2707, 3697, 4428, 4512,  5381,  5895
  259, 1440, 2050, 3360, 4755, 4924, 5408, 7387, 8851, 9020, 10757, 11783
  ...

Links

Crossrefs

Cf. A005187, A055938 (row 1), A256994 (column 1), A256989 (row index), A256990 (column index).
Inverse: A256998.
Transpose: A256995.
Cf. also A254107, A255557 (variants), A246278 (another thematically similar construction).

Programs

Formula

A(1,col) = A055938(col), and for row > 1, A(row,col) = A005187(A(row-1,col)).

A256995 Square array A(row,col) read by antidiagonals: A(row,1) = A055938(row), and for col > 1, A(row,col) = A005187(A(row,col-1)).

Original entry on oeis.org

2, 3, 5, 4, 8, 6, 7, 15, 10, 9, 11, 26, 18, 16, 12, 19, 49, 34, 31, 22, 13, 35, 95, 66, 57, 41, 23, 14, 67, 184, 130, 110, 79, 42, 25, 17, 131, 364, 258, 215, 153, 81, 47, 32, 20, 259, 723, 514, 424, 302, 159, 89, 63, 38, 21, 515, 1440, 1026, 844, 599, 312, 174, 120, 73, 39, 24, 1027, 2876, 2050, 1683, 1192, 620, 343, 236, 143, 74, 46, 27
Offset: 2

Views

Author

Antti Karttunen, Apr 14 2015

Keywords

Comments

The array is read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
This is transpose of array A256997.
If we assume that a(1) = 1 (but which is not explicitly included here because outside of the array proper), then A256996 gives the inverse permutation.

Examples

			The top left corner of the array:
   2,  3,  4,   7,  11,  19,   35,   67,  131,  259,   515,  1027
   5,  8, 15,  26,  49,  95,  184,  364,  723, 1440,  2876,  5745
   6, 10, 18,  34,  66, 130,  258,  514, 1026, 2050,  4098,  8194
   9, 16, 31,  57, 110, 215,  424,  844, 1683, 3360,  6716, 13425
  12, 22, 41,  79, 153, 302,  599, 1192, 2380, 4755,  9504, 19004
  13, 23, 42,  81, 159, 312,  620, 1235, 2464, 4924,  9841, 19675
  14, 25, 47,  89, 174, 343,  680, 1356, 2707, 5408, 10812, 21617
  17, 32, 63, 120, 236, 467,  928, 1852, 3697, 7387, 14765, 29521
  20, 38, 73, 143, 281, 558, 1111, 2216, 4428, 8851, 17696, 35388
  21, 39, 74, 145, 287, 568, 1132, 2259, 4512, 9020, 18033, 36059
  ...

Links

Crossrefs

Inverse permutation: A256996.
Transpose: A256997.
Cf. A005187, A055938 (column 1), A256994 (row 1), A256989 (column index), A256990 (row index).
Cf. also A254105, A255555 (variants), A114537, A246279 (other thematically similar constructions).

Programs

Formula

A(row,1) = A055938(row), and for col > 1, A(row,col) = A005187(A(row,col-1)).

A279342 a(0) = 1, a(1) = 2, a(2n) = A055938(a(n)), a(2n+1) = A005187(a(n)).

Original entry on oeis.org

1, 2, 5, 3, 12, 8, 6, 4, 27, 22, 17, 15, 13, 10, 9, 7, 58, 50, 45, 41, 36, 32, 30, 26, 28, 23, 21, 18, 20, 16, 14, 11, 121, 112, 103, 97, 92, 86, 84, 79, 75, 70, 65, 63, 61, 56, 55, 49, 59, 53, 48, 42, 44, 39, 37, 34, 43, 38, 33, 31, 29, 25, 24, 19, 248, 237, 227, 221, 210, 201, 196, 191, 187, 180, 175, 168, 171, 165, 160, 153, 154, 146, 141
Offset: 0

Views

Author

Antti Karttunen, Dec 10 2016

Keywords

Comments

Note the indexing: the domain starts from 0, while the range excludes zero.
This sequence can be represented as a binary tree. Each left hand child is produced as A055938(n), and each right hand child as A005187(n), when the parent node contains n:
1
|
...................2...................
5 3
12......../ \........8 6......../ \........4
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
27 22 17 15 13 10 9 7
58 50 45 41 36 32 30 26 28 23 21 18 20 16 14 11
etc.

Links

Crossrefs

Inverse: A279341.
Right edge: A256994.
Cf. A005187, A055938.
Related or similar permutations: A054429, A163511, A233278, A256997, A279339, A279344, A279347.

Programs

Formula

a(0) = 1, a(1) = 2, and then after, a(2n) = A055938(a(n)), a(2n+1) = A005187(a(n)).
As a composition of other permutations:
a(n) = A279344(A054429(n)).
a(n) = A279347(A279344(n)).
a(n) = A279339(A163511(n)).

A279344 a(0) = 1, a(2n) = A005187(a(n)), a(2n+1) = A055938(a(n)).

Original entry on oeis.org

1, 2, 3, 5, 4, 6, 8, 12, 7, 9, 10, 13, 15, 17, 22, 27, 11, 14, 16, 20, 18, 21, 23, 28, 26, 30, 32, 36, 41, 45, 50, 58, 19, 24, 25, 29, 31, 33, 38, 43, 34, 37, 39, 44, 42, 48, 53, 59, 49, 55, 56, 61, 63, 65, 70, 75, 79, 84, 86, 92, 97, 103, 112, 121, 35, 40, 46, 51, 47, 52, 54, 60, 57, 62, 64, 68, 73, 77, 82, 90, 66, 69, 71, 76, 74, 80
Offset: 0

Views

Author

Antti Karttunen, Dec 10 2016

Keywords

Comments

Note the indexing: the domain starts from 0, while the range excludes zero.
This sequence can be represented as a binary tree. Each left hand child is produced as A005187(n), and each right hand child as A055938(n), when the parent node contains n:
1
|
...................2...................
3 5
4......../ \........6 8......../ \........12
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
7 9 10 13 15 17 22 27
11 14 16 20 18 21 23 28 26 30 32 36 41 45 50 58
etc.

Links

Crossrefs

Inverse: A279343.
Left edge: A256994.
Cf. A005187, A055938.
Related or similar permutations: A005940, A054429, A233276, A256997, A279339, A279342, A279347.

Programs

Formula

a(0) = 1, after which, a(2n) = A005187(a(n)), a(2n+1) = A055938(a(n)).
As a composition of other permutations:
a(n) = A279342(A054429(n)).
a(n) = A279347(A279342(n)).
a(n) = A279339(A005940(1+n)).
Showing 1-4 of 4 results.

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