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 1-6 of 6 results.

A083927 Inverse function of N -> N injection A057123.

Original entry on oeis.org

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0
Offset: 0

Views

Author

Antti Karttunen, May 13 2003

Keywords

Comments

a(0)=0 because A057123(0)=0, but a(n) = 0 also for those n which do not occur as values of A057123. All positive natural numbers occur here once.
If g(n) = A083927(f(A057123(n))) then we can say that Catalan bijection g embeds into Catalan bijection f in scale n:2n, using the obvious binary tree -> general tree embedding. E.g. we have: A057163 = A083927(A057164(A057123(n))), A057117 = A083927(A072088(A057123(n))), A057118 = A083927(A072089(A057123(n))), A069770 = A083927(A072796(A057123(n))), A072797 = A083927(A072797(A057123(n))).

Links

Crossrefs

a(A057123(n)) = n for all n. Cf. A083925-A083926, A083928-A083929, A083935.

A083929 Inverse function of N -> N injection A083930.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Antti Karttunen, May 13 2003

Keywords

Comments

a(0)=0 because A083930(0)=0, but a(n) = 0 also for those n which do not occur as values of A083930. All positive natural numbers occur here once.
It appears that A071661(n) = A083929(A071663(A083930(n))) and A071662 = A083929(A071664(A083930(n))).

Crossrefs

a(A080930(n)) = n for all n. Cf. A083925-A083928, A083935.

Formula

a(n) = A083927(A083925(n)).

A083925 Inverse function of N -> N injection A057548.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, May 13 2003

Keywords

Comments

a(1)=0 because A057548(0)=1, but a(n) = 0 also for those n which do not occur as values of A057548. All positive natural numbers occur here once.

Crossrefs

a(A057548(n)) = n for all n. Cf. A083926-A083929, A083935.

Formula

a(n) = A083923(n)*A072771(n).

A083928 Inverse function of N -> N injection A080298.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Antti Karttunen, May 13 2003

Keywords

Comments

a(1)=0 because A080298(0)=1, but a(n) = 0 also for those n which do not occur as values of A080298. All positive natural numbers occur here once.
For example, A057163 = A083928(A057163(A080298(n))), i.e. Catalan bijection A057163 embeds into itself in scale n:2n+1 using the obvious zigzag-tree -> binary tree embedding.

Links

Crossrefs

a(A080298(n)) = n for all n. Cf. A083925-A083927, A083929, A083935.

A083926 Inverse function of N -> N injection A072795.

Original entry on oeis.org

0, 0, 1, 0, 2, 3, 0, 0, 0, 4, 5, 6, 7, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44
Offset: 0

Views

Author

Antti Karttunen, May 13 2003

Keywords

Comments

a(1)=0 because A072795(0)=1, but a(n) = 0 also for those n which do not occur as values of A072795. All positive natural numbers occur here once.

Crossrefs

a(A072795(n)) = n for all n. Cf. A083925, A083927-A083929, A083935.

Formula

a(n) = A083924(n)*A072772(n).

A083934 A014486-indices of A083932-trees.

Original entry on oeis.org

0, 3, 15, 22, 113, 120, 178, 185, 196, 1103, 1110, 1168, 1175, 1186, 1787, 1794, 1852, 1859, 1870, 2022, 2029, 2040, 2055, 12257, 12264, 12322, 12329, 12340, 12941, 12948, 13006, 13013, 13024, 13176, 13183, 13194, 13209, 20122, 20129, 20187
Offset: 0

Views

Author

Antti Karttunen, May 13 2003

Keywords

Crossrefs

Cf. A014486, A080300, A083932.
Inverse function: A083935.

Formula

a(n) = A080300(A083932(n)).
Showing 1-6 of 6 results.

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