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 1-4 of 4 results.

A275726 A275725-polynomials evaluated at x=2: a(n) = A048675(A275725(n)).

Original entry on oeis.org

1, 2, 5, 3, 4, 3, 11, 10, 7, 4, 5, 4, 9, 7, 7, 4, 6, 4, 8, 7, 6, 4, 5, 4, 23, 22, 21, 19, 20, 19, 15, 14, 9, 5, 6, 5, 11, 8, 9, 5, 8, 5, 9, 8, 7, 5, 6, 5, 19, 18, 15, 12, 13, 12, 15, 14, 9, 5, 6, 5, 13, 11, 9, 5, 7, 5, 12, 11, 8, 5, 6, 5, 17, 15, 15, 12, 14, 12, 13, 11, 9, 5, 7, 5, 11, 8, 9, 5, 8, 5, 10, 8, 8, 5, 7, 5
Offset: 0

Views

Author

Antti Karttunen, Aug 09 2016

Keywords

Links

Crossrefs

Cf. A000142, A048675, A055010, A275725.
Cf. A275833 (indices of odd terms), A275834 (of even terms).

Programs

Formula

a(n) = A048675(A275725(n)).
Other identities:
For n >= 1, a(n!) = A055010(n).

A275832 Size of the cycle containing element 1 in finite permutations listed in tables A060117 & A060118: a(n) = A007814(A275725(n)).

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Aug 11 2016

Keywords

Examples

			For n=0, the permutation with rank 0 in list A060118 is "1" (identity permutation) where 1 is fixed (in a 1-cycle), thus a(0)=1.
For n=1, the permutation with rank 1 in list A060118 is "21" where 1 is in a transposition (a 2-cycle), thus a(1)=2.
For n=3, the permutation with rank 3 in list A060118 is "231" where 1 is in a 3-cycle, thus a(3)=3.
For n=16, the permutation with rank 16 in list A060118 is "3412" (1 is in the other of two disjoint transpositions (1 3) and (2 4)), thus a(16)=2.
For n=44, the permutation with rank 44 in list A060118 is "43251", where 1 is a part of 3-cycle, thus a(44)=3.

Links

Crossrefs

Cf. A060117, A060118.
Cf. A000142, A007814, A033312, A275725, A275807.
Cf. A153880 (positions of 1's), A273670 (of terms larger than one), A275833 (of odd terms), A275834 (of even terms).

Programs

Formula

a(n) = A007814(A275725(n)).
Other identities:
For n >= 1, a(A033312(n)) = n.
For n >= 2, a(A000142(n)) = 1.

A275814 Positions of even terms in A060131; indices of permutations of an even order in tables A060117 & A060118.

Original entry on oeis.org

1, 2, 4, 6, 7, 9, 11, 12, 15, 16, 17, 18, 20, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 37, 38, 40, 43, 44, 46, 48, 49, 51, 53, 55, 56, 58, 60, 61, 62, 64, 66, 67, 68, 70, 72, 75, 76, 77, 78, 79, 80, 82, 85, 86, 88, 90, 91, 92, 94, 96, 98, 99, 101, 102, 103, 104, 106, 108, 109, 110, 112, 115, 116, 118, 120, 121, 122, 123, 124, 125
Offset: 1

Views

Author

Antti Karttunen, Aug 10 2016

Keywords

Links

Crossrefs

Complement: A275813.
Cf. A060117, A060118, A060131.
Cf. A275834 (a subsequence).

A275833 Positions of odd terms in A275832; indices of those permutations in tables A060117 & A060118 where element 1 is in an odd cycle.

Original entry on oeis.org

0, 2, 3, 5, 6, 8, 10, 12, 13, 14, 19, 22, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 52, 54, 56, 57, 59, 60, 61, 62, 63, 64, 65, 67, 69, 71, 72, 73, 74, 78, 79, 80, 81, 82, 83, 84, 86, 87, 89, 93, 94, 95, 97, 100, 103, 105, 107, 111, 112, 113, 114, 116, 117, 119, 120, 122, 123, 125, 126, 128, 130, 132, 133, 134, 139, 142, 144
Offset: 0

Views

Author

Antti Karttunen, Aug 11 2016

Keywords

Comments

Indexing starts from zero, because a(0)=0 is a special case in this sequence.
Equally: positions of odd terms in A275726.

Links

Crossrefs

Complement: A275834.
Cf. A153880 (a subsequence).
Cf. A275726, A275832.
Showing 1-4 of 4 results.

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