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.

A274307 Numbers n such that n^2 is a term of A274306.

This page as a plain text file.
%I A274307 #14 Jun 21 2016 14:17:43
%S A274307 1,325,7010415003293431191312386899866982908203125
%N A274307 Numbers n such that n^2 is a term of A274306.
%C A274307 The sequence is known to be infinite.
%C A274307 Once sufficiently many further terms are found, their indices in A274306 can give another sequence.
%C A274307 The terms' indices in A274306 are: 0, 3, 20, 119, 696, 4059, 23660, 137903, ... - _Chai Wah Wu_, Jun 20 2016
%C A274307 The terms' indices are equal to the sequence A001652 and thus satisfy a linear recurrence. Gürel showed that 2k^2+2k+1 = k^2 + (k+1)^2 is a square if and only if A274306(k) is a square, i.e, (k, k+1) are the 2 smaller terms of a Pythagorean triple and thus k is the index of a term if and only if it is in A001652. - _Chai Wah Wu_, Jun 21 2016
%H A274307 Erhan Gürel, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.123.6.597">On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products</a>, The American Mathematical Monthly 123.6 (2016): 597-599.
%Y A274307 Cf. A274306.
%K A274307 nonn
%O A274307 1,2
%A A274307 _N. J. A. Sloane_, Jun 20 2016