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 1-7 of 7 results.

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)))

A082320 Permutation A057502 applied four times ("^4"), permutation A082316 squared.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 8, 7, 5, 9, 14, 21, 18, 13, 10, 15, 20, 17, 12, 19, 16, 11, 22, 23, 37, 58, 49, 35, 24, 38, 57, 48, 34, 56, 47, 33, 64, 25, 39, 59, 50, 36, 26, 40, 54, 45, 31, 53, 44, 30, 63, 27, 41, 55, 46, 32, 51, 42, 28, 62, 52, 43, 29, 61, 60, 65, 107, 170, 142, 100
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082319. Occurs in A073200. Cf. also A082321-A082324.

Formula

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

A082315 Permutation A057501 applied twice ("squared").

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003, Proposed by Wouter Meeussen

Keywords

Links

Crossrefs

Inverse of A082316. a(n) = A082313(A057164(n)). Occurs in A073200 as row 34359740687. Cf. also A082317-A082324.
Number of cycles: A054357. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

Formula

a(n) = A057501(A057501(n)).

A085160 Permutation of natural numbers induced by the Catalan bijection gma085160 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 17, 10, 16, 18, 11, 20, 12, 14, 21, 13, 15, 19, 22, 23, 45, 24, 44, 46, 25, 48, 26, 42, 49, 27, 43, 47, 50, 28, 54, 29, 53, 55, 30, 57, 31, 37, 58, 32, 38, 56, 59, 33, 61, 34, 39, 62, 35, 40, 51, 63, 36, 41, 52, 60, 64, 65, 129, 66, 128, 130
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Comments

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

Links

Crossrefs

Inverse: A085159. a(n) = A085161(A085159(A085161(n))) = A085169(A082316(A085170(n))) = A074684(A082316(A074683(n))) = A085174(A085174(n)). Occurs in A073200. Cf. also A085165-A085168, A086430.
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).

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).

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))

A082322 Permutation A057502 applied five times ("^5").

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 5, 4, 6, 17, 20, 12, 10, 15, 16, 19, 11, 9, 14, 22, 21, 18, 13, 45, 54, 31, 26, 40, 44, 53, 30, 25, 39, 63, 59, 50, 36, 46, 55, 32, 27, 41, 42, 51, 28, 23, 37, 62, 58, 49, 35, 43, 52, 29, 24, 38, 61, 57, 48, 34, 60, 56, 47, 33, 64, 129, 157, 87, 73, 115
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082321. Occurs in A073200. Cf. also A082323-A082324.

Formula

a(n) = A082316(A082318(n))
Showing 1-7 of 7 results.

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

Content is available under The OEIS End-User License Agreement.