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 A345475 #14 Oct 30 2021 05:01:26 %S A345475 2,3,5,6,7,8,10,11,12,13,15,17,18,20,24,26,27,30,32,35,37,38,39,40,41, %T A345475 42,48,50,51,55,56,58,63,65,66,68,72,74,75,80,82,83,84,87,90,99,101, %U A345475 102,104,105,110,120,122,123,130,132,135,136,143,145,146,147 %N A345475 Nonsquares k whose continued fraction for the square root of k has a periodic part that is a nondecreasing sequence. %C A345475 All k = m^2 + 1 (A002522) belong in the sequence because the periodic part of the continued fraction of sqrt(k) has a single element. %e A345475 a(5)=7 because the periodic part of the continued fraction of sqrt(7) is (1,1,1,4) which is a nondecreasing sequence. %e A345475 19 is not a term because the periodic part of the continued fraction of sqrt(19) is (2, 1, 3, 1, 2, 8) which is not a nondecreasing sequence. %t A345475 Select[Range@147,!IntegerQ@Sqrt@#&&OrderedQ@Last@ContinuedFraction[Sqrt@#]&] %Y A345475 Cf. A003285, A002522, A121339. %K A345475 nonn %O A345475 1,1 %A A345475 _Giorgos Kalogeropoulos_, Sep 16 2021