A128926 Smaller member p of a pair of consecutive primes (p,q) such that either q^2-p^2+1 or q^2-p^2-1 is also prime.

3, 5, 7, 11, 17, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 73, 79, 83, 89, 101, 103, 107, 109, 113, 127, 131, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 199, 211, 223, 227, 229, 233, 241, 251, 257, 263, 281, 307, 311, 313, 331, 337, 353, 359, 367, 373, 379

Offset: 1

Author

J. M. Bergot, Apr 25 2007

Keywords

• nonn

Examples

			3 and 5 are consecutive primes, 5^2-3^2 = 25-9 = 16. 17 is prime, hence 3 is in the sequence.
79 and 83 are consecutive primes, 83^2-79^2 = 6889-6241 = 648. 647 is prime, hence 79 is in the sequence.
89 and 97 are consecutive primes, 97^2-89^2 = 9409-7921 = 1488. 1487 (as well as 1489) is prime, hence 89 is in the sequence.
		

Crossrefs

Cf. A069482.

Programs

Magma

[ p: p in PrimesUpTo(380) | IsPrime(q^2-p^2-1) or IsPrime(q^2-p^2+1) where q is NextPrime(p) ]; /* Klaus Brockhaus, May 05 2007 */

Maple

isA128926 := proc(n) local p,q ; p := ithprime(n) ; q := ithprime(n+1) ; isprime((p+q)*(q-p)+1) or isprime((p+q)*(q-p)-1) ; end:
for n from 1 to 100 do if isA128926(n) then printf("%d,",ithprime(n)) ; fi ; od ; # R. J. Mathar, Apr 26 2007

Mathematica

Prime@ Select[ Range@ 75, PrimeQ[ Prime[ # + 1]^2 - Prime@#^2 - 1] || PrimeQ[ Prime[ # + 1]^2 - Prime@#^2 + 1] &] (* Robert G. Wilson v *)

Extensions

Corrected and extended by Robert G. Wilson v, R. J. Mathar and Klaus Brockhaus, Apr 26 2007