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

1,1

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.

Links

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

Example

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

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 *)

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).

Sequence in context: A216073 A086870 A107693 * A122528 A123206 A035078

Adjacent sequences: A217714 A217715 A217716 * A217718 A217719 A217720

Keyword

nonn

Author

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

Status

approved