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URL: https://oeis.org/A284928

⇱ A284928 - OEIS

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A284928
Numbers k such that 2k + p is composite for all primes p, q with p + q = 2k.
2
0, 1, 2, 3, 14, 19, 26, 29, 31, 34, 37, 40, 41, 44, 47, 49, 56, 59, 61, 62, 64, 68, 73, 74, 76, 79, 82, 83, 86, 89, 91, 92, 94, 95, 103, 104, 106, 107, 109, 110, 112, 119, 121, 122, 124, 125, 128, 131, 134, 139, 142, 145, 146, 148, 149, 151, 152, 154, 158, 160, 161, 163, 164, 166, 169
OFFSET
1,3
COMMENTS
Or, numbers k such that there is no prime p < 2k with 2k - p and 2k + p both prime.
The two initial terms vacuously satisfy the definition, but all even numbers >= 4 are the sum of two primes, according to the Goldbach conjecture.
See also A284919, twice this sequence, which lists the values of 2k.
LINKS
Claudio Meller and others, New sequence, SeqFan list, April 5, 2017. (Click "next" for subsequent contributions.)
PROG
(PARI) is_A284928(n)=!forprime(p=2, n, isprime(2*n-p) && (isprime(2*n+p) || isprime(4*n-p)) && return) \\ M. F. Hasler, Apr 06 2017
CROSSREFS
Cf. A284919 (twice this), A002375 (number of decompositions p + q = 2k), A020481 (least p: p + q = 2k).
Sequence in context: A212112 A107083 A266694 * A374232 A294405 A160218
KEYWORD
nonn
AUTHOR
M. F. Hasler, Apr 06 2017
STATUS
approved