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 1-3 of 3 results.

A091452 Transpose of array in A091451 associated with period lengths of square roots of positive integers.

Original entry on oeis.org

1, 4, 2, 9, 5, 3, 16, 10, 6, 7, 25, 17, 8, 14, 13, 36, 26, 11, 23, 29, 19, 49, 37, 12, 28, 53, 21, 31, 64, 50, 15, 32, 74, 22, 44, 41, 81, 65, 18, 33, 85, 45, 69, 130, 43, 100, 82, 20, 34, 89, 52, 71, 268, 67, 46
Offset: 1

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Author

Clark Kimberling, Feb 03 2004

Keywords

Comments

A permutation of the positive integers.

Examples

			Northwest corner of array:
1 2 3 7
4 5 6 14
9 10 8 23
16 17 11 28
		

Crossrefs

A091449 Array T(n,k) read by antidiagonals, where row n is the increasing sequence of numbers m for which the simple continued fraction of sqrt(m) has period n, n >= 0, k >= 1.

Original entry on oeis.org

1, 2, 4, 3, 5, 9, 41, 6, 10, 16, 7, 130, 8, 17, 25, 13, 14, 269, 11, 26, 36, 19, 29, 23, 370, 12, 37, 49, 58, 21, 53, 28, 458, 15, 50, 64, 31, 73, 22, 74, 32, 697, 18, 65, 81, 106, 44, 202, 45, 85, 33, 986, 20, 82, 100, 43, 113, 69, 250, 52, 89, 34, 1313, 24, 101, 121
Offset: 0

Views

Author

Clark Kimberling, Feb 03 2004

Keywords

Comments

A permutation of the positive integers.

Examples

			Array begins:
  n\k|   1   2   3   4   5   6   7    8    9   10   11
  ---+------------------------------------------------
   0 |   1   4   9  16  25  36  49   64   81  100  121
   1 |   2   5  10  17  26  37  50   65   82  101  122
   2 |   3   6   8  11  12  15  18   20   24   27   30
   3 |  41 130 269 370 458 697 986 1313 1325 1613 1714
   4 |   7  14  23  28  32  33  34   47   55   60   62
   5 |  13  29  53  74  85  89 125  173  185  218  229
   6 |  19  21  22  45  52  54  57   59   70   77   88
   7 |  58  73 202 250 274 314 349  425  538  761 1010
   8 |  31  44  69  71  91  92 108  135  153  158  160
   9 | 106 113 137 149 265 389 493  610  698  754  970
  10 |  43  67  86  93 115 116 118  129  154  159  161
The least n for which CF(sqrt(n)) has period of length 4 is n=7, with CF=[2;1,1,1,4,1,1,1,4,1,1,1,4,...]; thus T(4,1)=7.
[The array T(n,k) is indexed by n=0,1,2,3,..., k=1,2,3... .]
Row 0 consists of squares: 1,4,9,...
		

Crossrefs

Rows 0-100 are: A000290 (except the initial 0), A002522 (except the initial 1), A013642, A013643, A013644, A010337, A020347, A010338, A020348, A010339, A020349-A020439.

Extensions

a(17) = T(3,3) corrected by Pontus von Brömssen, Nov 23 2024

A091450 Transpose of A091449: array T(n,k) read by antidiagonals, where column k is the increasing sequence of numbers m for which the simple continued fraction of sqrt(m) has period k, n >= 1, k >= 0.

Original entry on oeis.org

1, 4, 2, 9, 5, 3, 16, 10, 6, 41, 25, 17, 8, 130, 7, 36, 26, 11, 269, 14, 13, 49, 37, 12, 370, 23, 29, 19, 64, 50, 15, 458, 28, 53, 21, 58, 81, 65, 18, 697, 32, 74, 22, 73, 31, 100, 82, 20, 986, 33, 85, 45, 202, 44, 106, 121, 101, 24, 1313, 34, 89, 52, 250, 69, 113, 43
Offset: 1

Views

Author

Clark Kimberling, Feb 03 2004

Keywords

Comments

A permutation of the positive integers.

Examples

			Array begins:
  n\k|   0   1  2    3  4   5  6    7   8   9  10
  ---+-------------------------------------------
   1 |   1   2  3   41  7  13 19   58  31 106  43
   2 |   4   5  6  130 14  29 21   73  44 113  67
   3 |   9  10  8  269 23  53 22  202  69 137  86
   4 |  16  17 11  370 28  74 45  250  71 149  93
   5 |  25  26 12  458 32  85 52  274  91 265 115
   6 |  36  37 15  697 33  89 54  314  92 389 116
   7 |  49  50 18  986 34 125 57  349 108 493 118
   8 |  64  65 20 1313 47 173 59  425 135 610 129
   9 |  81  82 24 1325 55 185 70  538 153 698 154
  10 | 100 101 27 1613 60 218 77  761 158 754 159
  11 | 121 122 30 1714 62 229 88 1010 160 970 161
The least m for which CF(sqrt(m)) has period of length 4 is m=7, with CF=[2;1,1,1,4,1,1,1,4,1,1,1,4,...]; thus T(1,4)=7.
[The array T(n,k) is indexed by n=1,2,3,..., k=0,1,2,3... .]
Column 0 consists of squares: 1,4,9,...
		

Crossrefs

Extensions

a(19) = T(3,3) corrected by Pontus von Brömssen, Nov 23 2024
Showing 1-3 of 3 results.