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 1-10 of 167 results. Next

A130403 Signature permutations of SPINE-transformations of A057163-conjugates of Catalan automorphisms in table A122204.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 7, 3, 2, 1, 0, 6, 8, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 4, 7, 5, 4, 3, 2, 1, 0, 9, 5, 6, 6, 5, 4, 3, 2, 1, 0, 10, 17, 8, 8, 8, 5, 4, 3, 2, 1, 0, 11, 18, 9, 7, 6, 8, 5, 5, 3, 2, 1, 0, 12, 20, 10, 9, 7, 7, 7, 4, 4, 3, 2, 1, 0, 13, 21, 12, 10, 9, 6
Offset: 0

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Author

Antti Karttunen, Jun 11 2007

Keywords

Comments

Row n is the signature permutation of the Catalan automorphism which is obtained from A057163-conjugate of the n-th automorphism in the table A122204 with the recursion scheme "SPINE", i.e. row n is obtained as SPINE(A057163 o ENIPS(A089840[n]) o A057163). See A122203 and A122204 for the description of SPINE and ENIPS. Each row occurs only once in this table. Inverses of these permutations can be found in table A130402. This table contains also all the rows of A122203 and A089840.

Crossrefs

Cf. The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A082345, 2: A130936, 3: A073288, 4: A130942, 5: A130940, 6: A130938, 7: A130944, 8: A130946, 9: A130952, 10: A130950, 11: A130948, 12: A057161, 13: A130962, 14: A130964, 15: A069767, 16: A130966, 17: A074688, 18: A130954, 19: A130956, 20: A130960, 21: A130958, Other rows: 169: A069770, 3617: A082339, 65167: A057501.
Cf. also tables A089840, A122201-A122204, A122285-A122286, A130400-A130401.
Cf. As a sequence differs from A130403 for the first time at n=92, where a(n)=21, while A130403(n)=22.

A130402 Signature permutations of ENIPS-transformations of A057163-conjugates of Catalan automorphisms in table A122203.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 7, 3, 2, 1, 0, 6, 8, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 4, 7, 5, 4, 3, 2, 1, 0, 9, 5, 6, 6, 5, 4, 3, 2, 1, 0, 10, 17, 8, 8, 8, 5, 4, 3, 2, 1, 0, 11, 18, 9, 7, 6, 8, 5, 5, 3, 2, 1, 0, 12, 20, 10, 9, 7, 7, 7, 4, 4, 3, 2, 1, 0, 13, 22, 12, 10, 9, 6
Offset: 0

Views

Author

Antti Karttunen, Jun 11 2007

Keywords

Comments

Row n is the signature permutation of the Catalan automorphism which is obtained from A057163-conjugate of the n-th automorphism in the table A122203 with the recursion scheme "ENIPS", i.e. row n is obtained as ENIPS(A057163 o SPINE(A089840[n]) o A057163). See A122203 and A122204 for the description of SPINE and ENIPS. Each row occurs only once in this table. Inverses of these permutations can be found in table A130403. This table contains also all the rows of A122204 and A089840.

Crossrefs

Cf. The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A082346, 2: A130935, 3: A073289, 4: A130937, 5: A130939, 6: A130941, 7: A130943, 8: A130945, 9: A130947, 10: A130949, 11: A130951, 12: A074687, 13: A130953, 14: A130955, 15: A130957, 16: A130959, 17: A057162, 18: A130961, 19: A130963, 20: A130965, 21: A069768. Other rows: 251: A069770, 3613: A082340, 65352: A057502.
Cf. also tables A089840, A122201-A122204, A122285-A122286, A130400-A130401.
Cf. As a sequence differs from A130403 for the first time at n=92, where a(n)=22, while A130403(n)=21.

A082358 Permutation of natural numbers: composition of permutations A057163 & A082356.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Comments

This is the signature-permutation of Catalan automorphism which is derived from nonrecursive Catalan automorphism *A123496 with the recursion schema FORK (defined in A122201). - Antti Karttunen, Oct 11 2006

Links

Crossrefs

Inverse of A082357. Cf. also A082359-A082360.
See the Wolframesque plots of A122242 and A122245.
Row 65796 of table A122201.

Formula

a(n) = A057163(A082356(n))

A125977 Signature-permutation of a Catalan automorphism: composition of A057163 and A125976.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Links

Crossrefs

Inverse: A125978. a(n) = A057163(A125976(n)). The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A126317, A126318 and A126319. The number of fixed points seems to be given by A123050 and fixed points themselves are probably given by A126312. Cf. also A126313-A126316.
Differs from A071661 for the first time at n=43, where a(n)=40, while A071661(43)=34. Differs from A071666 for the first time at n=34, where a(n)=47, while A071666(34)=48.

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

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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))

A082357 Permutation of natural numbers: composition of permutations A082355 & A057163.

Original entry on oeis.org

0, 1, 3, 2, 7, 6, 8, 5, 4, 17, 16, 18, 15, 14, 22, 21, 20, 12, 11, 19, 13, 10, 9, 45, 44, 46, 43, 42, 50, 49, 48, 40, 39, 47, 41, 38, 37, 63, 62, 64, 59, 58, 61, 57, 54, 31, 30, 53, 32, 29, 28, 60, 56, 55, 36, 35, 52, 34, 26, 25, 51, 33, 27, 24, 23, 129, 128, 130, 127, 126
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082358. Cf. also A082359-A082360.

Formula

a(n) = A082355(A057163(n))

A082325 Permutation of natural numbers: A057163-conjugate of A057511.

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, 49, 48, 50, 44, 47, 42, 37, 38, 43, 40, 39, 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

Links

Crossrefs

Inverse of A082326. a(n) = A069787(A082326(A069787(n))). a(n) = A082327(A082853(n))+A082852(n). Occurs in A073200 as row 1792. Cf. also A082337-A082338.
Differs from A082342 first time at n=39: a(39)=49, while A082342(39)=48.
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).

Formula

a(n) = A057163(A057511(A057163(n)))

A082326 Permutation of natural numbers: A057163-conjugate of A057512.

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, 49, 48, 50, 44, 47, 42, 37, 38, 43, 40, 39, 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

Links

Crossrefs

Inverse of A082325. a(n) = A069787(A082325(A069787(n))). a(n) = A082328(A082853(n))+A082852(n). Occurs in A073200 as row 1794. Cf. also A082337-A082338.
Differs from A082341 first time at n=39: a(39)=49, while A082341(39)=48.
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).

Formula

a(n) = A057163(A057512(A057163(n)))

A125978 Signature-permutation of a Catalan automorphism: composition of A125976 and A057163.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 5, 6, 8, 9, 17, 12, 16, 21, 10, 18, 11, 14, 20, 13, 15, 19, 22, 23, 45, 31, 44, 58, 26, 49, 30, 42, 57, 35, 48, 56, 63, 24, 46, 32, 43, 59, 25, 47, 28, 37, 54, 34, 40, 53, 62, 27, 50, 29, 38, 55, 33, 39, 51, 61, 36, 41, 52, 60, 64, 65, 129, 87, 128, 170, 73
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2007

Keywords

Links

Crossrefs

Inverse: A125977. a(n) = A125976(A057163(n)).
Showing 1-10 of 167 results. Next

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