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A121339 Periodic part of continued fraction for square roots of integers.

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%I A121339 #14 Oct 09 2023 01:43:53
%S A121339 2,1,2,4,2,4,1,1,1,4,1,4,6,3,6,2,6,1,1,1,1,6,1,2,1,6,1,6,8,4,8,2,1,3,
%T A121339 1,2,8,2,8,1,1,2,1,1,8,1,2,4,2,1,8,1,3,1,8,1,8,10,5,10,3,2,3,10,2,1,1,
%U A121339 2,10,2,10,1,1,3,5,3,1,1,10,1,1,1,10,1,2,1,10,1,4,1,10,1,10,12,6,12,4,12
%N A121339 Periodic part of continued fraction for square roots of integers.
%H A121339 T. D. Noe, <a href="/A121339/b121339.txt">Rows n = 2..1000 of triangle, flattened</a>
%e A121339 The table starts:
%e A121339   2
%e A121339   1 2
%e A121339   <empty>
%e A121339   4
%e A121339   2 4
%e A121339   1 1 1 4
%e A121339   1 4
%t A121339 a[n_] := If[ IntegerQ[ Sqrt[n] ], {}, ContinuedFraction[ Sqrt[n] ] // Last]; Table[a[n], {n, 2, 39}] // Flatten (* _Jean-François Alcover_, Sep 10 2012 *)
%Y A121339 Cf. A003285 (row lengths), A013943 (row lengths for nonempty rows).
%K A121339 nice,nonn,tabf
%O A121339 2,1
%A A121339 _Franklin T. Adams-Watters_, Aug 28 2006