VOOZH about

URL: https://oeis.org/A091451

⇱ A091451 - OEIS

login
A091451
Array T(n,k) read by antidiagonals: (row 0)=squares, (row 1)={numbers m for which the simple continued fraction (CF) of sqrt(m) has period length 1}; once (row n) is defined, let (row n+1) begin with the least positive integer not already in a row and let the rest of (row n+1) be the other m's for which CF(sqrt(m)) has the same period length.
3
1, 2, 4, 3, 5, 9, 7, 6, 10, 16, 13, 14, 8, 17, 25, 19, 29, 23, 11, 26, 36, 31, 21, 53, 28, 12, 37, 49, 41, 44, 22, 74, 32, 15, 50, 64, 43, 130, 69, 45, 85, 33, 18, 65, 81, 46, 67, 269, 71, 52, 89, 34, 20, 82, 100, 58, 76, 86, 370, 91, 54, 125, 47, 24, 101, 121
OFFSET
0,2
COMMENTS
A permutation of the positive integers.
From Pontus von Brömssen, Nov 23 2024: (Start)
Rows of A091449 sorted by the first term.
First column gives indices of new terms of A003285.
(End)
EXAMPLE
7 is the least positive integer not in rows 0,1,2, so 7=T(3,0); the period length of sqrt(7) is 4, as is the case with T(3,1)=14, T(3,2)=23, etc.
Corner:
1 4 9 16 25 36 49 64
2 5 10 17 26 37 50 65
3 6 8 11 12 15 18 20
7 14 23 28 32 33 34 47
13 29 53 74 85 89 125 173
19 21 22 45 52 54 57 59
MATHEMATICA
Map[Map[#[[1]] &, #] &,
GatherBy[Map[{#, Flatten[ContinuedFraction[Sqrt[#]]]} &, Range[500]],
Length[#[[2]]] &]] (* Peter J. C. Moses, May 11 2023 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 03 2004
EXTENSIONS
a(47) = T(7,2) corrected by Clark Kimberling, May 20 2023
More terms from Pontus von Brömssen, Nov 23 2024
STATUS
approved