A217717 Primes of the form x^2 + y^2 - 1, where x and y are primes.

7, 17, 73, 97, 193, 241, 313, 337, 409, 457, 577, 1009, 1129, 1201, 1249, 1321, 1489, 1657, 1801, 1873, 2017, 2137, 2377, 2521, 2689, 2833, 2857, 3049, 3169, 3217, 3361, 3529, 3697, 3769, 3889, 4057, 4177, 4441, 4513, 4561, 4657, 5209, 5449, 5569, 5689, 5857

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, Mar 21 2013

Keywords

• nonn

Comments

Unlike primes of the form x^2+y^2 (A045637) which can be redefined as x^2+4, and primes of the form x^2+y^2+1 (A182475) which can be redefined as primes of the form x^2+10, this sequence appears to have no one-variable analog. In the preceding, x and y are prime.

Examples

			457 is in the sequence because it is a prime number, and 457 = 13^2 + 17^2 - 1.
		

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045637 (primes of the form p^2+4, where p is prime).

Cf. A182475 (primes of the form p^2+10, where p is prime).

Programs

Mathematica

mx = 25; Union[Select[Flatten[Table[Prime[a]^2 + Prime[b]^2 - 1, {a, mx}, {b, a, mx}]], # < Prime[mx]^2 && PrimeQ[#] &]] (* T. D. Noe, Mar 29 2013 *)