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URL: https://oeis.org/A098807

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A098807
Numbers k such that there exists a prime p for which p - k and p + k are also prime.
2
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
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
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Oct 06 2004
EXTENSIONS
Definition and offset corrected by Robert Israel, Mar 16 2026
STATUS
approved