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A274307 Numbers n such that n^2 is a term of A274306. 2
1, 325, 7010415003293431191312386899866982908203125 (list; graph; refs; listen; history; text; internal format)



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


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.


Cf. A274306.

Sequence in context: A097739 A203188 A048918 * A031516 A066128 A138816

Adjacent sequences:  A274304 A274305 A274306 * A274308 A274309 A274310




N. J. A. Sloane, Jun 20 2016



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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)