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 A308720 #22 Mar 11 2025 03:02:55
%S A308720 0,0,2,2,0,4,4,4,4,0,6,6,6,6,6,6,0,8,8,8,8,8,8,8,8,0,10,10,10,10,10,
%T A308720 10,10,10,10,10,0,12,12,12,12,12,12,12,12,12,12,12,12,0,14,14,14,14,
%U A308720 14,14,14,14,14,14,14,14,14,14,0,16,16,16,16,16,16,16
%N A308720 The maximum value in the continued fraction of sqrt(n), or 0 if there is no fractional part.
%C A308720 The continued fraction expansion of sqrt(n) is periodic, and the maximal element is the last element in the period, 2*floor(sqrt(n)).
%H A308720 Oskar Perron, <a href="https://archive.org/details/dielehrevondenk00perrgoog/page/n5">Die Lehre von den Kettenbrüchen</a>, B. G. Teubner (1913), section 24, p. 87.
%F A308720 a(k^2) = 0.
%F A308720 a(m) = 2 * floor(sqrt(m)) for nonsquare m.
%F A308720 a(n) = 2 * A320471(n) for n > 0.
%t A308720 {0} ~Join~ Table[2 Mod[Floor@ Sqrt@ n, Ceiling@ Sqrt@ n], {n, 100}] (* _Giovanni Resta_, Jun 29 2019 *)
%Y A308720 Cf. A000196, A003285, A096494.
%K A308720 nonn,easy
%O A308720 0,3
%A A308720 _Karl Fischer_, Jun 19 2019
%E A308720 More terms from _Giovanni Resta_, Jun 29 2019