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 A233593 #16 Jul 12 2021 02:03:35
%S A233593 7,13,14,19,21,22,23,28,29,31,32,33,34,41,43,46,47,52,53,54,55,57,58,
%T A233593 59,60,61,62,67,69,70,71,73,74,75,76,77,78,79,85,86,88,89,91,92,93,94,
%U A233593 95,96,97,98,103,106,107
%N A233593 Positive integers k such that the continued fraction expansion sqrt(k) = c(1) + c(1)/(c(2) + c(2)/(c(3) + c(3)/....)) is aperiodic.
%C A233593 For more details about this type of expansions, see A233582.
%C A233593 The cases with known periodic expansions, listed in A233592, all become periodic after just two leading terms. In contrast, the Blazys's expansion of sqrt(a(k)) for every member a(k) of this list remains aperiodic up to at least 1000 terms. It is therefore conjectured, though not proved, that these expansions are indeed aperiodic.
%H A233593 Stanislav Sykora, <a href="/A233593/b233593.txt">Table of n, a(n) for n = 1..200</a>
%H A233593 Stanislav Sykora, <a href="http://dx.doi.org/10.3247/sl4math13.001">Blazys' Expansions and Continued Fractions</a>, Stans Library, Vol.IV, 2013.
%H A233593 Stanislav Sykora, <a href="http://oeis.org/wiki/File:BlazysExpansions.txt">PARI/GP scripts for Blazys expansions and fractions</a>, OEIS Wiki.
%e A233593 Blazys's expansion of sqrt(7), A233587, is {2, 3, 30, 34, 111, ...}. Its first 1000 terms are all distinct. Hence, 7 is a term of this sequence.
%Y A233593 Cf. A233592.
%Y A233593 Cf. Blazys's expansions: A233582, A233584, A233585, A233586, A233587.
%K A233593 nonn
%O A233593 1,1
%A A233593 _Stanislav Sykora_, Jan 06 2014