A284928 Numbers k such that 2k + p is composite for all primes p, q with p + q = 2k.

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

Author

M. F. Hasler, Apr 06 2017

Keywords

• nonn

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.)

Crossrefs

Cf. A284919 (twice this), A002375 (number of decompositions p + q = 2k), A020481 (least p: p + q = 2k).

Programs

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