cp's OEIS Frontend

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.

A345475 Nonsquares k whose continued fraction for the square root of k has a periodic part that is a nondecreasing sequence.

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%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