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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A073284 Permutation of natural numbers induced by the Catalan bijection gma073284! acting on the parenthesizations encoded by A014486.

Original entry on oeis.org

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

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Author

Antti Karttunen, Jun 25 2002

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Inverse permutation: A073285. Occurs for first time in A073200 as row 20.
The scheme function gma072796! referred to below given in A072796.

A074687 Permutation of natural numbers induced by the Catalan bijection gmA074687! acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 6, 7, 8, 4, 5, 15, 14, 16, 17, 18, 19, 20, 22, 13, 9, 21, 10, 11, 12, 39, 40, 41, 37, 38, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 60, 61, 62, 34, 33, 63, 36, 27, 23, 56, 57, 64, 35, 24, 58, 26, 32, 29, 59, 25, 28, 30, 31, 113, 112, 114, 115, 116
Offset: 0

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Author

Antti Karttunen, Sep 11 2002

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Inverse of A074688 and also a(n) = A057163(A074688(A057163(n))). Cf. A074681-A074690. Occurs in A073200 as row 5572440.

A074689 Permutation of natural numbers induced by the Catalan bijection gmA074689! acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

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

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Author

Antti Karttunen, Sep 11 2002

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Inverse of A074690. a(n) = A057163(A074685(A057163(n))). Cf. A074681-A074688. Occurs in A073200.

A082319 Permutation A057501 applied four times ("^4"), permutation A082315 squared.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 5, 7, 6, 9, 14, 21, 18, 13, 10, 15, 20, 17, 12, 19, 16, 11, 22, 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, 70, 79, 84, 93
Offset: 0

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Author

Antti Karttunen, Apr 17 2003

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Inverse of A082320. Occurs in A073200. Cf. also A082321-A082324.

Formula

a(n) = A082315(A082315(n))

A082323 Permutation A057501 applied six times ("^6"), permutation A082317 squared, permutation A082315 cubed.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 10, 20, 19, 11, 22, 12, 17, 16, 13, 18, 14, 15, 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, 79, 107, 121, 149
Offset: 0

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Author

Antti Karttunen, Apr 17 2003

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Inverse of A082324. a(n) = A057501(A082321(n)). Occurs in A073200.

Formula

a(n) = A082317(A082317(n)) = A082315(A082315(A082315(n)))

A082332 Permutation of natural numbers induced by the composition of involutions A069888 & A057163. &F A082332 a(n) = A069888(A057163(n)).

Original entry on oeis.org

0, 1, 2, 3, 6, 4, 8, 5, 7, 19, 16, 11, 14, 9, 22, 21, 13, 15, 10, 18, 20, 12, 17, 60, 56, 47, 53, 44, 33, 30, 39, 51, 42, 25, 28, 37, 23, 64, 63, 59, 62, 58, 36, 35, 41, 52, 43, 27, 29, 38, 24, 50, 49, 55, 61, 57, 32, 34, 40, 26, 46, 48, 54, 31, 45, 191, 186, 172, 182, 168
Offset: 0

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Author

Antti Karttunen, Apr 17 2003

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Inverse of A082331. Occurs in A073200 as row 576469548397005071. Cf. also A082333-A082334.

A082359 Permutation of natural numbers: composition of permutations A074683 & A057163.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

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Crossrefs

Inverse of A082360. Occurs in A073200 as row 18764713496857. Cf. also A082357-A082358.

Formula

a(n) = A074683(A057163(n)).

A082360 Permutation of natural numbers: composition of permutations A057163 & A074684.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082359. Occurs in A073200. Cf. also A082357-A082358.

Formula

a(n) = A057163(A074684(n)).

A085162 Permutation of natural numbers induced by Catalan Automorphism *A085162.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 17, 16, 12, 21, 14, 15, 11, 10, 18, 20, 19, 13, 22, 23, 45, 44, 31, 58, 42, 43, 30, 26, 49, 57, 56, 35, 63, 37, 40, 39, 38, 41, 28, 29, 25, 24, 46, 48, 47, 32, 59, 54, 55, 53, 51, 52, 34, 33, 27, 50, 62, 61, 60, 36, 64, 65, 129, 128, 87, 170
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

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a(n) = A057163(A085161(A057163(n))). Cf. also A085165, A085166, A086431. Occurs in A073200.
Number of cycles: A007123. Number of fixed points: A001405 (in each range limited by A014137 and A014138).

A085165 A057163-conjugate of A085159.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 12, 16, 17, 21, 10, 18, 11, 14, 15, 13, 19, 20, 22, 23, 26, 30, 31, 35, 42, 43, 44, 45, 49, 56, 57, 58, 63, 24, 32, 47, 46, 59, 25, 48, 28, 37, 38, 29, 39, 40, 41, 27, 50, 33, 51, 52, 34, 53, 54, 55, 36, 60, 61, 62, 64, 65, 68, 72, 73, 77
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2003

Keywords

Links

Crossrefs

Inverse: A085166. a(n) = A057163(A085159(A057163(n))) = A085162(A085166(A085162(n))). Occurs in A073200. Cf. also A085162, A086429, 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).
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