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.

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A073286 Permutation of natural numbers induced by the composition of the Catalan bijections A069770 & A069767.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Inverse permutation: A073287. Occurs for first time in A073200 as row 41. Counts of the fixed elements: A073268.

Formula

a(n) = A069770(A069767(n)).

A082324 Permutation A057502 applied six times ("^6"), permutation A082318 squared, permutation A082316 cubed.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 16, 19, 21, 22, 18, 17, 20, 13, 12, 10, 15, 23, 28, 37, 42, 51, 58, 62, 49, 46, 55, 35, 32, 27, 41, 24, 29, 38, 43, 52, 57, 61, 48, 45, 54, 34, 31, 26, 40, 56, 60, 47, 44, 53, 33, 30, 25, 39, 64, 63, 59, 50, 36, 65, 79, 107, 121, 149
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082323. a(n) = A057502(A082322(n)). Occurs in A073200.

Formula

a(n) = A082318(A082318(n)) = A082316(A082316(A082316(n)))

A082339 Permutation of natural numbers induced by the Catalan bijection gma082339 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082340. Occurs in A073200 as row 1796. Cf. also A072797, A082337-A082341.
Max. cycle size and LCMs of cycle sizes: A016116 (to be checked). (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A082333 Permutation of natural numbers induced by the composition of involutions A057163 & A082313.

Original entry on oeis.org

0, 1, 3, 2, 8, 4, 6, 5, 7, 22, 10, 19, 12, 17, 20, 9, 15, 13, 18, 14, 11, 21, 16, 64, 27, 60, 32, 46, 61, 25, 52, 35, 49, 51, 30, 58, 44, 62, 26, 53, 31, 45, 55, 24, 41, 36, 50, 39, 33, 59, 47, 54, 23, 40, 34, 48, 38, 29, 63, 56, 37, 28, 57, 43, 42, 196, 78, 191, 92, 134
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003, Proposed by Wouter Meeussen

Keywords

Links

Crossrefs

Cf. A057163, A082313.
Inverse of A082334. Occurs in A073200 as row 730750818666116073099889616808727458479087976635. Cf. also A082331-A082332.

Formula

a(n) = A057163(A082313(n)).

A082334 Permutation of natural numbers induced by the composition of involutions A082313 & A057163.

Original entry on oeis.org

0, 1, 3, 2, 5, 7, 6, 8, 4, 15, 10, 20, 12, 17, 19, 16, 22, 13, 18, 11, 14, 21, 9, 52, 43, 29, 38, 24, 61, 57, 34, 40, 26, 48, 54, 31, 45, 60, 56, 47, 53, 44, 64, 63, 36, 41, 27, 50, 55, 32, 46, 33, 30, 39, 51, 42, 59, 62, 35, 49, 25, 28, 37, 58, 23, 178, 164, 136, 155, 127
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082333. Occurs in A073200. Cf. also A082331-A082332.

Formula

a(n) = A082313(A057163(n))

A082345 Permutation of natural numbers induced by the Catalan bijection gma082345 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 6, 4, 5, 17, 18, 20, 21, 22, 16, 19, 14, 9, 10, 15, 11, 13, 12, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 44, 47, 53, 56, 60, 42, 51, 37, 23, 24, 38, 25, 27, 26, 43, 52, 39, 28, 29, 41, 33, 35, 36, 40, 30, 34, 32, 31, 129, 130, 132, 133, 134
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082346. Occurs in A073200 as row 66. Cf. also A069767, A073288-A073289, A082347-A082348.

A085163 Permutation of natural numbers induced by the Catalan bijection gma085163 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 11, 14, 16, 19, 17, 20, 12, 10, 18, 21, 15, 13, 22, 23, 25, 28, 30, 33, 37, 39, 42, 44, 56, 51, 53, 47, 60, 45, 48, 54, 57, 61, 31, 34, 26, 24, 46, 49, 38, 32, 59, 58, 62, 40, 29, 55, 35, 43, 27, 50, 63, 52, 41, 36, 64, 65, 67, 70, 72, 75
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Links

Crossrefs

Inverse: A085164. a(n) = A085161(A057508(n)). Occurs in A073200. Cf. also A085171, A085172. Scheme-function app-to-xrt given in A085203.
Number of fixed points 1, 1, 2, 2, 3, 4, 7, 11, 21, 36, 71, ... in range [A014137(n-1)..A014138(n-1)] of this permutation appears to be A051920 after the initial two ones.

A086430 Permutation of natural numbers induced by the Catalan bijection gma086430 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 11, 14, 16, 19, 17, 18, 12, 10, 15, 20, 21, 13, 22, 23, 25, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 45, 46, 48, 49, 50, 31, 32, 26, 24, 29, 40, 38, 43, 52, 54, 55, 57, 58, 59, 34, 35, 27, 41, 61, 62, 63, 36, 64, 65, 67, 70, 72, 75
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Comments

This Catalan bijection rotates the interpretations (pp)-(rr) of Stanley, using the "descending slope" mapping illustrated in A086431.

Links

Crossrefs

Inverse: A086429. a(n) = A086428(A086428(n)) = A086431(A086429(A086431(n))) = A057164(A085160(A057164(n))) = A086425(A082316(A086426(n))). Occurs in A073200.
Number of cycles: A054357. Number of fixed points: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A073194 Permutation of natural numbers induced by the Catalan bijection gmA073194 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 11, 14, 16, 19, 17, 20, 10, 12, 15, 21, 13, 18, 22, 23, 25, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 45, 48, 54, 57, 61, 26, 27, 24, 31, 34, 38, 40, 43, 52, 58, 62, 32, 35, 41, 46, 29, 49, 55, 63, 36, 50, 59, 64, 65, 67, 70, 72, 75, 79, 81
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073195. The car/cdr-flipped conjugate of A073205, i.e. A073194(n) = A057163(A073205(A057163(n))). Cf. also A073196-A073199.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073199 Permutation of natural numbers induced by the Catalan bijection gmA073199 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 16, 12, 17, 20, 10, 18, 11, 14, 15, 13, 19, 21, 22, 23, 44, 31, 42, 53, 30, 43, 26, 45, 49, 34, 54, 57, 61, 24, 47, 32, 46, 55, 25, 48, 28, 37, 38, 29, 39, 40, 41, 27, 50, 33, 51, 52, 35, 56, 58, 59, 36, 60, 62, 63, 64, 65, 126, 87, 128, 156, 68
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073198. The car/cdr-flipped conjugate of A073210, i.e. A073199(n) = A057163(A073210(A057163(n))). Cf. also A073194-A073197.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.
Previous Showing 21-30 of 91 results. Next

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