When the n-th term of this sequence is added to or subtracted from the square of the n-th prime of the form 4k + 1 (i.e., A002144(n)), the result in both cases is a square.
This sequence and A002144 give rise to a class of monic polynomials x^2 + bx + c where b = +- A002144(n) and c = +- a(n)/4 that will factor over the integers regardless of the sign of c. For example, x^2 - 13x - 30 and x^2 - 13x + 30 are two such polynomials. Further polynomials with this property can be found by transforming the roots.
