%I #14 Jun 21 2016 14:17:43

%S 1,325,7010415003293431191312386899866982908203125

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

%C The sequence is known to be infinite.

%C Once sufficiently many further terms are found, their indices in A274306 can give another sequence.

%C The terms' indices in A274306 are: 0, 3, 20, 119, 696, 4059, 23660, 137903, ... - _Chai Wah Wu_, Jun 20 2016

%C 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 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 Cf. A274306.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jun 20 2016