A351863 Numbers k with at least one divisor, d, such that k-d is prime.

3, 4, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 30, 32, 34, 38, 42, 44, 46, 48, 54, 58, 60, 62, 68, 72, 74, 80, 82, 84, 86, 90, 94, 98, 102, 104, 106, 108, 110, 114, 118, 122, 128, 132, 134, 138, 140, 142, 146, 150, 152, 158, 164, 166, 168, 174, 178, 180, 182, 192, 194, 198, 200, 202

Offset

1,1

Links

Table of n, a(n) for n=1..64.

Formula

Apparently, a(n) = 2*(A179182(n-1) + 1) for n >= 2. - Hugo Pfoertner, Feb 23 2022

Example

4 is in the sequence since 4-(1)=3, 4-(2)=2, 4-(4)=0, and at least one of 3,2,0 is prime.
56 is not in the sequence since the divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, and none of 56-1, 56-2, 56-4, ... etc. are prime (i.e., none of 55, 54, 52, 49, 48, 42, 28, 0 are prime).

Mathematica

q[n_] := AnyTrue[Divisors[n], PrimeQ[n - #] &]; Select[Range[200], q] (* Amiram Eldar, Feb 22 2022 *)

Prog

(PARI) isok(k) = sumdiv(k, d, isprime(k-d)) >= 1; \\ Michel Marcus, Feb 22 2022
(PARI) is(n) = isprime(n-1) || (n%2 == 0 && isprime(n/2)) \\ David A. Corneth, Feb 22 2022
(Python)
from sympy import divisors, isprime
def ok(n): return any(isprime(n-d) for d in divisors(n))
print([k for k in range(203) if ok(k)]) # Michael S. Branicky, Feb 22 2022

Crossrefs

Cf. A242932.

Union of A008864 and A100484.

Sequence in context: A156624 A341340 A242932 * A025201 A071259 A231405

Adjacent sequences: A351860 A351861 A351862 * A351864 A351865 A351866

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 22 2022

Status

approved