Squares of form 2 n^2 - 1

Theorem

The sequence of integers $\left\langle{n}\right\rangle$ such that $2 n^2 - 1$ is square begins:

$1, 5, 29, 169, 985, 5741, 33461, 195025, 1136689, 6625109, \ldots$

This sequence is A001653 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

This theorem requires a proof. In particular: Follows somehow from the fact that these numbers are the hypotenuses of Definition:Almost Isosceles Pythagorean Triangles. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $29$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $29$