A224888 Primes of the form p^2 + (q-p)^2, where p and q are consecutive primes.

5, 13, 29, 293, 997, 6257, 11897, 18773, 19421, 52457, 73477, 109597, 120413, 167381, 192737, 218233, 249017, 292717, 333029, 361237, 398261, 466553, 502781, 546137, 552113, 591377, 635353, 683933, 687341, 704117, 737897, 885517, 966353, 982117, 1018097, 1079621

Offset: 1

Author

Thomas Ordowski, Jul 24 2013

Keywords

• nonn

Comments

Primes of the form A000040(n)^2 + A001223(n)^2.

Primes of the form A134735(2n-1)^2 + A134735(2n)^2.

Conjecture: a(n) ~ A093343(n).

There are 20421247 members of this sequence below 10^20. - Charles R Greathouse IV, Jul 29 2013

Examples

			3 and 5 are consecutive primes and 3^2 + (5-3)^2 = 9 + 4 = 13 is prime, so 13 is in the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A093343.

Programs

Mathematica

Select[Table[Prime[n]^2 + (Prime[n + 1] - Prime[n])^2, {n, 200}], PrimeQ] (* Alonso del Arte, Jul 29 2013 *)

PARI

p=2;forprime(q=3,1e4,if(isprime(t=p^2+(q-p)^2),print1(t", "));p=q) \\ Charles R Greathouse IV, Jul 24 2013

Formula

c(x) is O( sqrt(x/log x) / log x ), where c(x) is the counting function, the number of terms less than x.

Extensions

a(5), a(9)-a(36) from Charles R Greathouse IV, Jul 24 2013