A179484 Primes p such that p+-180 are squares.

181, 349, 2029, 8101

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 16 2010

Keywords

• nonn
• fini
• full

Comments

Sequences of this type searching for p+d=s^2, p-d=t^2 (here: d=180) are finite because the difference 2d=(s+t)(s-t) has a finite set of solutions -- found by scanning the divisors of 2d (see A060829, A061409). [R. J. Mathar, Jul 20 2010]

Examples

			181-180=1^2;181+180=19^2;349-180=13^2,349+180=23^2;2029-180=43^2,2029+180=47^2;8101-180=89^2,8101+180=91^2;
		

Programs

Mathematica

q=180;Select[Table[Prime[n],{n,3*9!}],IntegerQ[Sqrt[ #-q]]&&IntegerQ[Sqrt[ #+q]]&]

Extensions

keyword:fini,full inserted - Zak Seidov and R. J. Mathar, Jul 19 2010