A098807 Numbers k such that there exists a prime p for which p - k and p + k are also prime.

2, 4, 6, 8, 10, 12, 14, 18, 20, 24, 28, 30, 34, 36, 38, 40, 42, 48, 50, 54, 60, 64, 66, 68, 72, 78, 80, 84, 90, 94, 96, 98, 102, 104, 108, 110, 114, 120, 124, 126, 132, 134, 138, 144, 150, 154, 156, 162, 164, 168, 174, 178, 180, 186, 188, 190, 192, 198, 204, 208, 210

Offset

1,1

Comments

From Robert Israel, Mar 16 2026: (Start)

All terms are even.

Dickson's Conjecture implies that all multiples of 6 are terms.

An even number k not divisible by 3 is a term if and only if k + 3 and 2*k + 3 are primes. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(4) = 8 is a term because p = 11, p - 8 = 3 and p + 8 = 19 are primes. - Robert Israel, Mar 16 2026

Maple

filter:= proc(k)
k mod 3 = 0 or (isprime(k + 3) and isprime(2*k+3))
end proc:
select(filter, [seq(i, i=2..1000, 2)]); # Robert Israel, Mar 16 2026

Crossrefs

Cf. A098806.

Sequence in context: A276106 A321501 A238264 * A189562 A194372 A058218

Adjacent sequences: A098804 A098805 A098806 * A098808 A098809 A098810

Keyword

easy,nonn

Author

Cino Hilliard, Oct 06 2004

Extensions

Definition and offset corrected by Robert Israel, Mar 16 2026

Status

approved