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 k's for which CF(sqrt(k)) has the same period length.

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

Offset

1,2

Comments

A permutation of the positive integers.

Links

Table of n, a(n) for n=1..55.

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

Cf. A091449, A091453.

Sequence in context: A349947 A351652 A333087 * A365389 A246161 A245701

Adjacent sequences: A091448 A091449 A091450 * A091452 A091453 A091454

Keyword

nonn,tabl,more

Author

Clark Kimberling, Feb 03 2004

Extensions

a(66) corrected by Clark Kimberling, May 20 2023

Status

approved