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.
%I A091451 #25 Nov 24 2024 09:26:20
%S A091451 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,
%T A091451 37,49,41,44,22,74,32,15,50,64,43,130,69,45,85,33,18,65,81,46,67,269,
%U A091451 71,52,89,34,20,82,100,58,76,86,370,91,54,125,47,24,101,121
%N 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.
%C A091451 A permutation of the positive integers.
%C A091451 From _Pontus von Brömssen_, Nov 23 2024: (Start)
%C A091451 Rows of A091449 sorted by the first term.
%C A091451 First column gives indices of new terms of A003285.
%C A091451 (End)
%e A091451 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.
%e A091451 Corner:
%e A091451 1 4 9 16 25 36 49 64
%e A091451 2 5 10 17 26 37 50 65
%e A091451 3 6 8 11 12 15 18 20
%e A091451 7 14 23 28 32 33 34 47
%e A091451 13 29 53 74 85 89 125 173
%e A091451 19 21 22 45 52 54 57 59
%t A091451 Map[Map[#[[1]] &, #] &,
%t A091451 GatherBy[Map[{#, Flatten[ContinuedFraction[Sqrt[#]]]} &, Range[500]],
%t A091451 Length[#[[2]]] &]] (* _Peter J. C. Moses_, May 11 2023 *)
%Y A091451 Cf. A003285, A091449, A091453.
%K A091451 nonn,tabl
%O A091451 0,2
%A A091451 _Clark Kimberling_, Feb 03 2004
%E A091451 a(47) = T(7,2) corrected by _Clark Kimberling_, May 20 2023
%E A091451 More terms from _Pontus von Brömssen_, Nov 23 2024