cp's OEIS Frontend

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.

%I A091450 #12 Dec 13 2024 14:14:05
%S A091450 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,
%T A091450 23,29,19,64,50,15,458,28,53,21,58,81,65,18,697,32,74,22,73,31,100,82,
%U A091450 20,986,33,85,45,202,44,106,121,101,24,1313,34,89,52,250,69,113,43
%N 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.
%C A091450 A permutation of the positive integers.
%e A091450 Array begins:
%e A091450   n\k|   0   1  2    3  4   5  6    7   8   9  10
%e A091450   ---+-------------------------------------------
%e A091450    1 |   1   2  3   41  7  13 19   58  31 106  43
%e A091450    2 |   4   5  6  130 14  29 21   73  44 113  67
%e A091450    3 |   9  10  8  269 23  53 22  202  69 137  86
%e A091450    4 |  16  17 11  370 28  74 45  250  71 149  93
%e A091450    5 |  25  26 12  458 32  85 52  274  91 265 115
%e A091450    6 |  36  37 15  697 33  89 54  314  92 389 116
%e A091450    7 |  49  50 18  986 34 125 57  349 108 493 118
%e A091450    8 |  64  65 20 1313 47 173 59  425 135 610 129
%e A091450    9 |  81  82 24 1325 55 185 70  538 153 698 154
%e A091450   10 | 100 101 27 1613 60 218 77  761 158 754 159
%e A091450   11 | 121 122 30 1714 62 229 88 1010 160 970 161
%e A091450 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.
%e A091450 [The array T(n,k) is indexed by n=1,2,3,..., k=0,1,2,3... .]
%e A091450 Column 0 consists of squares: 1,4,9,...
%Y A091450 Cf. A002522, A013642, A091449, A091451, A091453.
%K A091450 nonn,tabl
%O A091450 1,2
%A A091450 _Clark Kimberling_, Feb 03 2004
%E A091450 a(19) = T(3,3) corrected by _Pontus von Brömssen_, Nov 23 2024