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 A259911 #11 Nov 28 2024 11:14:18
%S A259911 5,12,12,21,8,21,8,60,60,8,5,24,13,24,5,60,140,12,12,140,60,77,12,285,
%T A259911 5,285,12,77,24,28,44,120,120,44,28,24,13,5,21,168,29,168,21,5,13,140,
%U A259911 44,168,56,1020,1020,56,168,44,140,165,120,93,8,1365,40,1365,8,93,120,165
%N A259911 Triangular array; row k shows the discriminant of the field of the number having purely periodic continued fraction with period (j,k+1-j), for j=1..k.
%H A259911 Clark Kimberling, <a href="/A259911/b259911.txt">Table of n, a(n) for n = 1..1000</a>
%e A259911 First eight rows:
%e A259911 5
%e A259911 12 12
%e A259911 21 8 21
%e A259911 8 60 60 8
%e A259911 5 24 13 24 5
%e A259911 60 140 12 12 140 60
%e A259911 77 12 285 5 285 12 77
%e A259911 24 28 44 120 120 44 28 24
%e A259911 The number whose continued fraction is periodic with period (1,1) is the golden ratio, (1+sqrt(5))/2, so that the number in row 1 is 5.
%e A259911 As a square array A(n,k) read by antidiagonals, where A(n,k) corresponds to the continued fraction with pure period (n,k):
%e A259911 5, 12, 21, 8, 5, 60, 77, 24, ...
%e A259911 12, 8, 60, 24, 140, 12, 28, 5, ...
%e A259911 21, 60, 13, 12, 285, 44, 21, 168, ...
%e A259911 8, 24, 12, 5, 120, 168, 56, 8, ...
%e A259911 5, 140, 285, 120, 29, 1020, 1365, 440, ...
%e A259911 60, 12, 44, 168, 1020, 40, 1932, 156, ...
%e A259911 77, 28, 21, 56, 1365, 1932, 53, 840, ...
%e A259911 24, 5, 168, 8, 440, 156, 840, 17, ...
%e A259911 ...
%t A259911 v = Table[FromContinuedFraction[{j, {k + 1 - j, j}}], {k, 1, 20}, {j, 1, k}];
%t A259911 TableForm[NumberFieldDiscriminant[v]]
%Y A259911 Cf. A259912 (main diagonal of square array), A259913 (first column).
%K A259911 nonn,tabl,easy
%O A259911 1,1
%A A259911 _Clark Kimberling_, Jul 20 2015