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

1,1

Comments

All terms are == 0 (mod 6).

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Subsequence of A177833 and of A075190.

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

Sequence in context: A119240 A257722 A093247 * A199924 A215950 A192770

Adjacent sequences: A248782 A248783 A248784 * A248786 A248787 A248788

Keyword

nonn

Author

Zak Seidov, Oct 13 2014

Extensions

More terms from Michel Marcus, Oct 14 2014

Status

approved