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.

A216870 A maximal length five arithmetic progression of squares in a quadratic number field.

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%I A216870 #14 Dec 04 2018 11:03:22
%S A216870 49,169,289,409,529
%N A216870 A maximal length five arithmetic progression of squares in a quadratic number field.
%C A216870 Bremner (2102): "Xarles (2011) investigated arithmetic progressions (APs) in number fields, and proved the existence of an upper bound K(d) for the maximal length of an AP of squares in a number field of degree d. He shows that K(2) = 5."
%C A216870 Euler showed that K(1) = 3. See A216869 for the smallest non-constant example. Another example is a(1), a(2), a(3) = 49, 169, 289 = 7^2, 13^2, 17^2.
%C A216870 It is known that K(3) >= 4.
%H A216870 A. Bremner, <a href="http://jointmathematicsmeetings.org/amsmtgs/2141_abstracts/1086-11-296.pdf">Arithmetic progressions of squares in cubic fields</a>, Abstract 2012.
%H A216870 X. Xarles, <a href="http://arxiv.org/abs/0909.1642">Squares in arithmetic progression over number fields</a>, arXiv:0909.1642 [math.AG], 2009.
%H A216870 X. Xarles, <a href="https://doi.org/10.1016/j.jnt.2011.07.010">Squares in arithmetic progression over number fields</a>, J. Number Theory, 132 (2012), 379-389.
%F A216870 a(n+1) - a(n) = 120 for n = 1, 2, 3, 4.
%e A216870 a(n) = 7^2, 13^2, 17^2, sqrt(409)^2, 23^2 for n = 1, 2, 3, 4, 5.
%t A216870 NestList[120+#&,49,4] (* _Harvey P. Dale_, Apr 20 2013 *)
%Y A216870 Cf. A216869, A221671, A221672.
%K A216870 nonn,fini,full
%O A216870 1,1
%A A216870 _Jonathan Sondow_, Nov 20 2012