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

1, 325, 7010415003293431191312386899866982908203125

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

Table of n, a(n) for n=1..3.

Erhan Gürel, On the Occurrence of Perfect Squares Among Values of Certain Polynomial Products, The American Mathematical Monthly 123.6 (2016): 597-599.

Crossrefs

Cf. A274306.

Sequence in context: A097739 A203188 A048918 * A358148 A031516 A066128

Adjacent sequences: A274304 A274305 A274306 * A274308 A274309 A274310

Keyword

nonn

Author

N. J. A. Sloane, Jun 20 2016

Status

approved