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.

A355424 Positive integers m such that the real quadratic fields of the form Q(sqrt(m^2+4)) have class number 1.

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%I A355424 #18 Jul 03 2022 09:10:14
%S A355424 1,3,5,7,13,17
%N A355424 Positive integers m such that the real quadratic fields of the form Q(sqrt(m^2+4)) have class number 1.
%C A355424 Former Yokoi's conjecture, proved by Biró in 2003 (see References). There are only six real quadratic fields of the form Q(sqrt(a(n)^2+4)), where Q indicates the set of rational numbers, with class number one.
%H A355424 A. Biró, <a href="http://dx.doi.org/10.4064/aa106-1-6">Yokoi's conjecture</a>, Acta Arith., vol. 106(1), 2003, pp. 85-104.
%F A355424 Let n be a positive integer less than 7. a(n) = 4*n - 7 iff n = 5, 6 and a(n) = 1 + 2*(n - 1) otherwise.
%e A355424 a(1) = 1, since h(1^2 + 4) = h(5) = 1.
%Y A355424 Cf. A050950, A053329, A308420.
%K A355424 nonn,fini,full
%O A355424 1,2
%A A355424 _Marco Ripà_, Jul 01 2022