A248785 Numbers n with the property that p = n^2 - 13 and q = n^2 + 13 are consecutive primes.

948, 1134, 1500, 2058, 2856, 3192, 3846, 3906, 4842, 5190, 5502, 6744, 6888, 7266, 7392, 7698, 8586, 8778, 8850, 9198, 9558, 10272, 10500, 10782, 11658, 11730, 11760, 12456, 12738, 13062, 13578, 14130, 14262, 14658, 14808, 15306, 15552, 15720, 16104, 16242

Offset: 1

Author

Zak Seidov, Oct 13 2014

Keywords

• nonn

Comments

All terms are == 0 (mod 6).

Examples

			n = 948, p = 898691 = prime(71194), q = 898717 = prime(71195);
n = 1134, p = 1285943 = prime(99033), q = 1285969 = prime(99034).
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1278

Crossrefs

Subsequence of A177833 and of A075190.

E.g., a(1) = 948 = A075190(103) = A177833(15).

Programs

Maple

with(numtheory): A248785:=n->`if`(isprime(n^2-13) and isprime(n^2+13) and pi(n^2+13) = pi(n^2-13)+1,n,NULL): seq(A248785(n), n=1..2*10^4); # Wesley Ivan Hurt, Oct 13 2014

Mathematica

Select[Range[17000],PrimeQ[#^2-13]&&NextPrime[#^2-13]==#^2+13&] (* Harvey P. Dale, Aug 14 2020 *)

PARI

isok(n) = isprime(p=n^2-13) && isprime(q=n^2+13) && (q==nextprime(p+1)); \\ Michel Marcus, Oct 14 2014

Extensions

More terms from Michel Marcus, Oct 14 2014