A128925 Primes p such that at least one of the two numbers p^2 - 6, p^2 + 6 is prime.

3, 5, 7, 11, 13, 17, 19, 23, 31, 47, 53, 61, 67, 73, 79, 83, 89, 97, 107, 109, 113, 131, 151, 167, 193, 197, 199, 263, 269, 293, 317, 331, 367, 373, 383, 401, 431, 457, 463, 467, 487, 503, 557, 569, 593, 607, 643, 647, 673, 677, 683, 709, 773, 787, 797, 823, 827

Offset

1,1

Comments

p = 5 is the only term for which both p^2 - 6 and p^2 + 6 are primes.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

5^2 - 6 = 19 is prime (just as is 5^2+6 = 31), hence 5 is in the sequence.
79^2 + 6 = 6241 + 6 = 6247 is prime, hence 79 is in the sequence.
83^2 - 6 = 6889 - 6 = 6883 is prime, hence 83 is in the sequence.

Maple

a:=proc(n) if isprime(ithprime(n)^2+6)=true or isprime(ithprime(n)^2-6)=true then ithprime(n) else fi end: seq(a(n), n=1..200); # Emeric Deutsch, May 05 2007

Mathematica

Select[ Prime@ Range[2, 145], PrimeQ[ #^2 - 6] || PrimeQ[ #^2 + 6] &] (* Robert G. Wilson v, May 01 2007 *)

Prog

(PARI) {forprime(p=2, 830, s=p^2; if(isprime(s-6)||isprime(s+6), print1(p, ", ")))} /* Klaus Brockhaus, May 06 2007 */

Crossrefs

Cf. A001248 (squares of primes).

Sequence in context: A338132 A120334 A000978 * A204142 A131261 A100276

Adjacent sequences: A128922 A128923 A128924 * A128926 A128927 A128928

Keyword

nonn

Author

J. M. Bergot, Apr 25 2007

Extensions

Edited and extended by Robert G. Wilson v, Klaus Brockhaus and Emeric Deutsch, May 01 2007

Status

approved