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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A073208 Permutation of natural numbers induced by the Catalan bijection gmA073208 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 16, 10, 14, 19, 17, 18, 12, 11, 15, 20, 13, 21, 22, 23, 26, 42, 44, 53, 25, 38, 37, 24, 47, 27, 51, 56, 60, 45, 48, 49, 46, 50, 31, 32, 30, 28, 39, 40, 43, 29, 52, 54, 55, 34, 33, 41, 57, 35, 58, 59, 61, 36, 62, 63, 64, 65, 126, 73, 72, 76, 121
Offset: 0

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Author

Antti Karttunen, Jun 25 2002

Keywords

Comments

Is there an equivalent Catalan bijection in A073200?

Links

Crossrefs

Inverse permutation: A073207. The car/cdr-flipped conjugate of A073197, i.e. A073208(n) = A057163(A073197(A057163(n))). Cf. also A073205-A073210.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.

A073280 Self-inverse permutation of natural numbers induced by the composition of the Catalan bijections A069770 & A057163.

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 6, 8, 7, 13, 12, 11, 10, 9, 15, 14, 19, 22, 21, 16, 20, 18, 17, 36, 35, 34, 32, 31, 33, 30, 29, 27, 26, 28, 25, 24, 23, 41, 40, 39, 38, 37, 52, 51, 60, 64, 63, 56, 62, 59, 58, 43, 42, 53, 61, 57, 47, 55, 50, 49, 44, 54, 48, 46, 45, 106, 105, 104, 101, 100
Offset: 0

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Author

Antti Karttunen, Jun 25 2002

Keywords

Links

Crossrefs

Occurs for first time in A073200 as row 9.

Formula

a(n) = A069770(A057163(n)) = A057163(A069770(n)).

A074688 Permutation of natural numbers induced by the Catalan bijection gmA074688! acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 4, 5, 6, 18, 20, 21, 22, 17, 10, 9, 11, 12, 13, 14, 15, 19, 16, 50, 55, 61, 57, 49, 62, 59, 63, 64, 58, 46, 45, 54, 48, 26, 27, 23, 24, 25, 29, 28, 30, 31, 32, 33, 34, 35, 36, 38, 37, 39, 40, 41, 51, 52, 56, 60, 42, 43, 44, 47, 53, 148, 162, 167, 181, 147
Offset: 0

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Author

Antti Karttunen, Sep 11 2002

Keywords

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Crossrefs

Inverse of A074687 and also a(n) = A057163(A074687(A057163(n))). Cf. A074681-A074690. Occurs in A073200.

A074690 Permutation of natural numbers induced by the Catalan bijection gmA074690! acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 6, 7, 8, 5, 4, 14, 15, 16, 17, 18, 19, 20, 22, 11, 12, 21, 13, 10, 9, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 60, 61, 62, 28, 29, 63, 30, 31, 32, 56, 57, 64, 33, 34, 59, 36, 25, 26, 58, 35, 27, 24, 23, 107, 108, 109, 110, 111
Offset: 0

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Author

Antti Karttunen, Sep 11 2002

Keywords

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Crossrefs

Inverse of A074689. a(n) = A057163(A074686(A057163(n))). Cf. A074681-A074688. Occurs in A073200.

A082321 Permutation A057501 applied five times ("^5").

Original entry on oeis.org

0, 1, 3, 2, 7, 6, 8, 4, 5, 17, 12, 16, 11, 22, 18, 13, 14, 9, 21, 15, 10, 20, 19, 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, 138, 157, 166, 180
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

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Crossrefs

Inverse of A082322. Occurs in A073200. Cf. also A082323-A082324.

Formula

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

A082341 Permutation of natural numbers induced by the Catalan bijection gma082341 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, 21, 19, 22, 23, 24, 26, 25, 27, 31, 32, 30, 28, 29, 34, 35, 33, 36, 45, 46, 48, 49, 50, 44, 47, 42, 37, 38, 43, 39, 40, 41, 54, 55, 57, 58, 59, 53, 56, 51, 52, 61, 62, 63, 60, 64, 65, 66, 68, 67, 69
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Comments

This is A057163-conjugate of A073285.

Links

Crossrefs

Inverse of A082342. a(n) = A057163(A073285(A057163(n))). Occurs in A073200 as row 1800. Cf. also A072797, A082337-A082339.
Differs from A082326 first time at n=39: a(39)=48, while A082326(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).

A082347 Permutation of natural numbers induced by the Catalan bijection gma082347 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082348. Occurs in A073200 as row 86. Cf. also A069768, A073288-A073289, A082345-A082346.

A082348 Permutation of natural numbers induced by the Catalan bijection gma082348 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082347. Occurs in A073200 as row 68. Cf. also A069767, A073288-A073289, A082345-A082346.

A086428 Permutation of natural numbers induced by the Catalan bijection gma086428 acting on symbolless S-expressions encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 5, 6, 4, 22, 20, 21, 18, 17, 13, 12, 15, 19, 16, 10, 11, 14, 9, 64, 61, 62, 55, 54, 63, 57, 59, 50, 49, 58, 46, 48, 45, 36, 34, 35, 32, 31, 41, 40, 52, 60, 53, 43, 56, 47, 44, 27, 26, 29, 33, 30, 38, 39, 51, 42, 24, 25, 28, 37, 23, 196, 192, 193, 181, 180
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 "descending slope" mapping illustrated in A086431.

Links

Crossrefs

Inverse: A086427. a(n) = A086431(A086427(A086431(n))) = A057164(A085174(A057164(n))) = A086425(A057502(A086426(n))). Occurs in A073200. Cf. also A086430 (whole step rotate).
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).

A073196 Permutation of natural numbers induced by the Catalan bijection gmA073196 acting on the parenthesizations as ordered by A014486.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 10, 14, 16, 19, 17, 21, 12, 11, 15, 18, 13, 20, 22, 23, 24, 25, 26, 27, 37, 38, 42, 44, 53, 51, 56, 47, 60, 45, 46, 58, 49, 59, 31, 34, 30, 28, 29, 40, 39, 43, 52, 48, 62, 35, 33, 41, 57, 32, 54, 63, 55, 36, 61, 50, 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: A073197. The car/cdr-flipped conjugate of A073207, i.e. A073196(n) = A057163(A073207(A057163(n))). Cf. also A073194-A073199.
The scheme functions gma072796! and gma072797! referred to below are given in A072796 and A072797.
Previous Showing 51-60 of 91 results. Next

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