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A248785 Numbers n with the property that p = n^2 - 13 and q = n^2 + 13 are consecutive primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 13 06:11 EDT 2021. Contains 343836 sequences. (Running on oeis4.)