A248790 Numbers k with the property that p = k^2 - 11 and q = k^2 + 11 are consecutive primes.

510, 720, 1200, 2190, 4350, 4980, 5040, 5250, 5670, 6810, 8280, 8490, 9150, 10140, 10650, 11430, 12510, 13800, 13980, 14160, 14640, 14700, 14820, 15000, 15750, 16890, 17220, 18180, 18270, 18750, 19110, 20940, 21270, 22050, 24000, 24570, 24720, 24990, 25620, 25920, 26520

Offset

1,1

Comments

All terms are == 0 (mod 30).

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

k=510, p=260089=prime(22845), q=260111=prime(22846).

Maple

q:= n-> (p-> isprime(p) and nextprime(p)-22=p)(n^2-11):
select(q, [$1..27000])[];  # Alois P. Heinz, Jan 14 2026

Mathematica

Select[Range[30000], With[{c=#^2-11}, PrimeQ[c]&&NextPrime[c]==c+22&]] (* Harvey P. Dale, Apr 03 2025 *)

Prog

(PARI) isok(n) = isprime(p=n^2-11) && isprime(q=n^2+11) && (q==nextprime(p+1)); \\ Michel Marcus, Oct 14 2014

Crossrefs

Subsequence of A176683 and of A075190. E.g., a(1)=510=A075190(62)=A176683(6).

Cf. A248785.

Sequence in context: A048254 A303994 A249551 * A252877 A202595 A252882

Adjacent sequences: A248787 A248788 A248789 * A248791 A248792 A248793

Keyword

nonn

Author

Zak Seidov, Oct 14 2014

Status

approved