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 1-7 of 7 results.

A084500 a(0)=0, after which each n occurs A084506(n) times.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23
Offset: 0

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Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Also minimum i such that A084505(i) >= n. Tells that the n-th throw (n>=1) in A084501 belongs to the a(n)-th lexicographical solution A084502(a(n)).

Links

Crossrefs

Differs from A084557 first time at the 605th term, where A084500(605) = 130, while A084557(605) = 131. Cf. A084510, A084520.

A084505 Partial sums of A084506.

Original entry on oeis.org

0, 1, 3, 5, 8, 11, 14, 17, 20, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 124, 129, 134, 139, 144, 149, 154, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239, 244, 249
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

For n>=1, (a(n-1)+1,a(n)) = (1,1),(2,3),(4,5),(6,8),(9,11),(12,14),... gives the starting and ending offsets of the n-th site swap in the sequence A084501.
Note: this sequence is related to juggling with three objects. For a similar sequence related to (ordinary) permutations, see A084555.

Links

Crossrefs

Differs from A084555 first time at the 130th term, where A084505(130) = 605, while A084555(130) = 604.
A084503(a(n)) = 7 for all n. However, this does not give the positions of all 7s in A084503 because the state sequences are not all indecomposable. Cf. A084515, A084525.

Extensions

Added the b-file, moved the misplaced Mathematica code to A084555, where it belongs. - Antti Karttunen, Oct 24 2012

A084508 Partial sums of A084509. Positions of ones in the first differences of A084506.

Original entry on oeis.org

0, 1, 3, 9, 33, 129, 513, 2049, 8193, 32769, 131073, 524289, 2097153, 8388609, 33554433, 134217729, 536870913, 2147483649, 8589934593, 34359738369, 137438953473, 549755813889, 2199023255553, 8796093022209, 35184372088833
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Cf. A084506, A084509, A087289.

Programs

  • Mathematica
    LinearRecurrence[{5,-4},{0,1,3,9},30] (* Harvey P. Dale, May 21 2021 *)

Formula

a(n) = n for n < 2, a(n) = 2^(2*n - 3) + 1 = A087289(n-2) for n >= 2. - Antti Karttunen, Oct 24 2012 [Corrected by Petros Hadjicostas, Aug 02 2020]
From Chai Wah Wu, Jan 28 2021: (Start)
a(n) = 5*a(n-1) - 4*a(n-2) for n > 3.
G.f.: x*(-2*x^2 - 2*x + 1)/((x - 1)*(4*x - 1)). (End)

A084556 n occurs n! times.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Also minimum i such that A007489(i) >= n.
For n>=1, a(n) gives the length of the n-th permutation in the sequences like A030298 & A030496.

Links

Crossrefs

First differences of A084555. Used to compute A084557. Differs from A084506 first time at the 130th term, where A084506(130) = 6, while A084556(130) = 5. Cf. also A002024, A072643, A072649, A090529.

Programs

  • Mathematica
    Flatten[ Table[#, {#!}] & /@ Range[0, 5]]

A084516 The length of each successively larger, indecomposable 3-ball ground-state site swap given in A084511, i.e., the number of digits in each term of A084512.

Original entry on oeis.org

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Partial sums: A084515. Differs from A084526 first time at the 18th term, where A084516(18) = 4, while A084526(18) = 5. Cf. also A084506, A084510, A084518.

A084526 The length of each successively larger, indecomposable, 'prime' 3-ball ground-state site swap given in A084521, i.e., the number of digits in each term of A084522.

Original entry on oeis.org

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Partial sums: A084525. Differs from A084516 first time at the 18th term, where A084516(18) = 4, while A084526(18) = 5. Cf. also A084506, A084520, A084528.

A084502 Successively larger 3-ball ground-state site swaps of A084501 in concatenated decimal notation.

Original entry on oeis.org

3, 33, 42, 333, 342, 423, 441, 522, 531, 3333, 3342, 3423, 3441, 3522, 3531, 4233, 4242, 4413, 4440, 4512, 4530, 5223, 5241, 5313, 5340, 5511, 5520, 6222, 6231, 6312, 6330, 6411, 6420, 33333, 33342, 33423, 33441, 33522, 33531, 34233, 34242, 34413
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Note that this decimal representation works only up to the A084500(A084507(10))-1 = 7707th term which is 99600000, after which follows the 7708th solution 10,2,2,2,2,2,2,2 which would be usually represented as "A2222222".

Links

Crossrefs

The number of 'digits' in term a(n) is given by A084506.
The number of terms of length n is given by A084509.
Cf. A084512, A084522.
Showing 1-7 of 7 results.

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