A091450 - OEIS

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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.

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

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OFFSET

1,2

COMMENTS

A permutation of the positive integers.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

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

Cf. A002522, A013642, A091449, A091451, A091453.

Sequence in context: A091452 A194032 A191739 * A163253 A191663 A206561

Adjacent sequences: A091447 A091448 A091449 * A091451 A091452 A091453

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 03 2004

EXTENSIONS

a(18) = T(3,3) corrected by Pontus von Brömssen, Nov 23 2024

STATUS

approved