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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 1-3 of 3 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

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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.

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).

A083924 Characteristic function for A072795.

Original entry on oeis.org

0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 0

Views

Author

Antti Karttunen, May 13 2003

Keywords

Comments

The sequence obtained by counting the runs of 0- and 1-bits 1,2,1,2,3,5,9,14,28,... is essentially the sequence A000108 interleaved with the sequence A000245, which appears to be A026008.

Links

Crossrefs

a(n) = A083923(A069770(n)). Used to compute A083926.

Formula

a(0) = 0, a(n>0) = 1 if A072771(n)=0, otherwise 0.
Showing 1-3 of 3 results.

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