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

1,1

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

Links

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

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A093343.

Sequence in context: A147492 A182069 A085555 * A256314 A002768 A354292

Adjacent sequences: A224885 A224886 A224887 * A224889 A224890 A224891

Keyword

nonn

Author

Thomas Ordowski, Jul 24 2013

Extensions

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

Status

approved