A256387 Numbers n such that no prime can be the arithmetic mean of 2 semiprimes whose difference is 2*n.

5, 7, 11, 13, 17, 19, 21, 23, 25, 29, 31, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, 55, 59, 61, 63, 65, 67, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 137, 139, 141, 143

Offset

1,1

Comments

That is, there is no prime p, such that p+n and p-n are both semiprime.

Complement of A256389.

From Robert Israel, Apr 13 2020: (Start)

Includes odd number n if and only if n+4 is not prime or 2*n+4 is not a semiprime.

There any no even members up to 10^5. Conjecture: all members are odd. (End)

Links

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

Example

A256383 is the list of numbers n such that n-5 and n+5 are semiprimes, and it contains no prime, hence 5 is in the sequence.

Maple

select(t -> not isprime(t+4) or numtheory:-bigomega(2*t+4) <> 2, [seq(i, i=1..1000, 2)]); # Robert Israel, Apr 13 2020

Crossrefs

Cf. A256383.

Cf. A256388 (a single prime), A256389 (one or more primes).

Sequence in context: A270998 A342105 A035035 * A113909 A111906 A348471

Adjacent sequences: A256384 A256385 A256386 * A256388 A256389 A256390

Keyword

nonn

Author

Michel Marcus, Mar 27 2015

Status

approved