OFFSET
1,2
COMMENTS
The sequence is known to be infinite.
Once sufficiently many further terms are found, their indices in A274306 can give another sequence.
The terms' indices in A274306 are: 0, 3, 20, 119, 696, 4059, 23660, 137903, ... - Chai Wah Wu, Jun 20 2016
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
LINKS
Erhan Gürel, On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products, The American Mathematical Monthly 123.6 (2016): 597-599.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 20 2016
STATUS
approved