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

1, 325, 7010415003293431191312386899866982908203125

Offset: 1

Author

N. J. A. Sloane, Jun 20 2016

Keywords

• nonn

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

Cf. A274306.