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.

A084506 The length of each successively larger 3-ball ground-state site swap given in A084501, i.e., the number of digits in each term of A084502.

Original entry on oeis.org

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, 5
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

Keywords

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Crossrefs

Partial sums: A084505.
Differs from A084556 first time at the 130th term, where A084506(130) = 6, while A084556(130) = 5.
Cf. A084516, A084526, A084500, A084508.

A084557 a(0)=0, after which each n occurs A084556(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

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Also minimum i such that A084555(i) >= n.
For n>=1, a(n) tells that the n-th term in A030298 belongs to the a(n):th lexicographically ordered permutation.

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Crossrefs

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

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".

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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.

A084510 a(0)=0, after which each n occurs A084516(n) times.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 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, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Also minimum i such that A084515(i) >= n. Tells that the n-th throw (n>=1) in A084511 belongs to the a(n)-th lexicographical solution A084512(a(n)).

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Differs from A084520 first time at the 65th term, where A084510(65) = 19, while A084520(65) = 18.
Cf. A084500.

A084520 a(0)=0, after which each n occurs A084526(n) times.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 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, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Also minimum i such that A084525(i) >= n. Tells that the n-th throw (n>=1) in A084521 belongs to the a(n)-th lexicographical solution A084522(a(n)).

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Differs from A084510 first time at the 65th term, where A084510(65) = 19, while A084520(65) = 18. Cf. A084500.

A005041 A self-generating sequence.

Original entry on oeis.org

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

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Author

N. J. A. Sloane, Jeffrey Shallit

Keywords

Comments

See A008620 for run lengths: each k occurs A008620(k+2) times. - Reinhard Zumkeller, Mar 16 2012

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A005038, A005039, A005040, A005043, A005044, A055086, A001462, A082462, A024417, A084500.

Programs

  • Haskell
    a005041 n = a005041_list !! n
a005041_list = 1 : f 1 1 (tail ts) where
   f y i gs'@((j,a):gs) | i < j  = y : f y (i+1) gs'
                        | i == j = a : f a (i+1) gs
   ts = [(6*k + 3*k*(k-1) `div` 2 + r*(k+2), 3*k+r+1) |
         k <- [0..], r <- [0,1,2]]
-- Reinhard Zumkeller, Mar 16 2012
  • Mathematica
    Table[n+1, {n, 0, 20}, {Ceiling[(n+1)/3]+1}] // Flatten (* Jean-François Alcover, Dec 10 2014 *)

Formula

For any k in {0, 1, 2, ...} and r in {0, 1, 2}, we have: if n = 6*k + (3/2)*k*(k-1) + r*(k+2), then a(n) = 3*k + r + 1. E.g., for k=3 and r=1, we have n = 6*3 + (3/2)*3*(3-1) + 1*(3+2) = 32 and so a(32) = 3*3 + 1 + 1 = 11. - Francois Jooste (phukraut(AT)hotmail.com), Mar 12 2002

Extensions

More terms from Samuel Hilliard (sam_spade1977(AT)hotmail.com), Apr 11 2004
Showing 1-6 of 6 results.

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