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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A085173 Permutation of natural numbers induced by the Catalan bijection gma085173 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 5, 6, 4, 22, 21, 18, 20, 17, 13, 12, 15, 19, 14, 10, 16, 11, 9, 64, 63, 59, 62, 58, 50, 49, 55, 61, 54, 46, 57, 48, 45, 36, 35, 32, 34, 31, 41, 40, 52, 60, 51, 38, 56, 39, 37, 27, 26, 43, 47, 42, 29, 53, 33, 28, 24, 44, 30, 25, 23, 196, 195, 190, 194, 189
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Comments

This Catalan bijection rotates by "half step" the interpretations (pp)-(rr) of Stanley, using the "rising slope" mapping illustrated in A085161.

Links

Crossrefs

Inverse: A085174. a(n) = A085161(A085174(A085161(n))) = A085169(A057501(A085170(n))) = A074684(A057501(A074683(n))). Occurs in A073200. Cf. also A085159 (whole step rotate), A086427.
Number of cycles: A002995. Number of fixed points: A019590. Max. cycle size: A057543. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A073195 Permutation of natural numbers induced by the Catalan bijection gmA073195 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 16, 10, 17, 20, 11, 18, 12, 14, 21, 13, 15, 19, 22, 23, 44, 24, 42, 43, 25, 57, 26, 45, 53, 27, 46, 54, 61, 28, 47, 29, 48, 55, 30, 49, 31, 37, 56, 32, 38, 58, 62, 33, 50, 34, 39, 59, 35, 40, 51, 63, 36, 41, 52, 60, 64, 65, 126, 66, 128, 131, 67
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073194. The car/cdr-flipped conjugate of A073206, i.e. A073195(n) = A057163(A073206(A057163(n))). Cf. also A073194-A073199.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073198 Permutation of natural numbers induced by the Catalan bijection gmA073198 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 14, 16, 11, 19, 17, 18, 10, 12, 15, 20, 13, 21, 22, 23, 37, 42, 30, 51, 44, 47, 28, 25, 39, 53, 33, 56, 60, 45, 46, 48, 49, 50, 26, 29, 24, 31, 40, 38, 43, 32, 52, 54, 55, 27, 34, 41, 57, 35, 58, 59, 61, 36, 62, 63, 64, 65, 107, 121, 70, 149, 126
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073199. The car/cdr-flipped conjugate of A073209, i.e. A073198(n) = A057163(A073209(A057163(n))). Cf. also A073194-A073197.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073206 Permutation of natural numbers induced by the Catalan bijection gmA073206 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 14, 16, 10, 19, 17, 18, 12, 11, 13, 20, 21, 15, 22, 23, 37, 42, 24, 51, 44, 47, 26, 25, 27, 53, 56, 38, 60, 45, 46, 48, 49, 50, 31, 32, 30, 28, 33, 34, 35, 39, 36, 54, 55, 57, 58, 59, 40, 29, 43, 52, 61, 62, 63, 41, 64, 65, 107, 121, 66, 149, 126
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073205. The car/cdr-flipped conjugate of A073195, i.e. A073206(n) = A057163(A073195(A057163(n))). Cf. also A073207-A073210.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073209 Permutation of natural numbers induced by the Catalan bijection gmA073209 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073210. The car/cdr-flipped conjugate of A073198, i.e. A073209(n) = A057163(A073198(A057163(n))). Cf. also A073205-A073208.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073282 Permutation of natural numbers induced by the composition of the Catalan bijections A072796 & A057163.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 5, 6, 4, 22, 21, 20, 18, 17, 13, 12, 15, 19, 16, 11, 14, 10, 9, 64, 63, 62, 59, 58, 61, 57, 55, 50, 49, 54, 48, 46, 45, 36, 35, 34, 32, 31, 41, 40, 52, 60, 56, 43, 53, 47, 44, 33, 30, 39, 51, 42, 29, 38, 27, 26, 28, 37, 25, 24, 23, 196, 195, 194, 190, 189
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Inverse permutation: A073283. Occurs for first time in A073200 as row 13.

Formula

a(n) = A072796(A057163(n))

A073283 Permutation of natural numbers induced by the composition of the Catalan bijections A057163 & A072796.

Original entry on oeis.org

0, 1, 3, 2, 8, 6, 7, 5, 4, 22, 21, 19, 15, 14, 20, 16, 18, 13, 12, 17, 11, 10, 9, 64, 63, 62, 59, 58, 60, 56, 52, 41, 40, 51, 39, 38, 37, 61, 57, 53, 43, 42, 55, 47, 50, 36, 35, 49, 34, 32, 31, 54, 44, 48, 33, 30, 46, 29, 27, 26, 45, 28, 25, 24, 23, 196, 195, 194, 190, 189
Offset: 0

Views

Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Inverse permutation: A073282. Occurs for first time in A073200 as row 19.

Formula

a(n) = A057163(A072796(n))

A082318 Permutation A057502 applied thrice ("cubed").

Original entry on oeis.org

0, 1, 3, 2, 7, 5, 6, 4, 8, 17, 12, 16, 11, 22, 18, 13, 14, 9, 21, 15, 10, 20, 19, 45, 31, 44, 30, 63, 46, 32, 42, 28, 62, 43, 29, 61, 60, 48, 34, 47, 33, 64, 49, 35, 37, 23, 58, 38, 24, 57, 56, 50, 36, 39, 25, 59, 40, 26, 54, 53, 41, 27, 55, 51, 52, 129, 87, 128, 86, 189
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082317. Occurs in A073200 as row 730750818665451459101842418728548123849399632523. Cf. also A082319-A082324.

Formula

a(n) = A057502(A082316(n))

A082331 Permutation of natural numbers induced by the composition of involutions A057163 & A069888.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 4, 8, 6, 13, 18, 11, 21, 16, 12, 17, 10, 22, 19, 9, 20, 15, 14, 36, 50, 33, 59, 47, 34, 48, 29, 63, 56, 28, 57, 43, 42, 35, 49, 30, 58, 44, 32, 46, 27, 64, 60, 25, 61, 52, 51, 31, 45, 26, 62, 53, 24, 55, 41, 39, 23, 54, 40, 38, 37, 106, 148, 102, 176, 144
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003, Proposed by Wouter Meeussen

Keywords

Comments

a(n) = A057163(A069888(n))

Links

Crossrefs

Inverse of A082332. Occurs in A073200 as row 9223512774351650875. Cf. also A082333-A082334.

A082342 Permutation of natural numbers induced by the Catalan bijection gma082342 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, 21, 19, 20, 22, 23, 24, 26, 25, 27, 31, 32, 30, 28, 29, 35, 33, 34, 36, 45, 46, 48, 49, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 58, 59, 56, 51, 52, 57, 53, 54, 55, 63, 60, 61, 62, 64, 65, 66, 68, 67, 69
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Comments

This is A057163-conjugate of A073284.

Links

Crossrefs

Inverse of A082341. a(n) = A057163(A073284(A057163(n))). Occurs in A073200. Cf. also A072797, A082337-A082339.
Differs from A082325 first time at n=39: a(39)=48, while A082325(39)=49.
Number of cycles: A057513. Number of fixed-points: A057546. Max. cycle size: A000793. LCM of cycle sizes: A003418. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).
Previous Showing 71-80 of 91 results. Next

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