A350496 Positive integers k such that if p is the largest prime less than k then k - p is prime.

5, 7, 9, 10, 13, 15, 16, 19, 21, 22, 25, 26, 28, 31, 33, 34, 36, 39, 40, 43, 45, 46, 49, 50, 52, 55, 56, 58, 61, 63, 64, 66, 69, 70, 73, 75, 76, 78, 81, 82, 85, 86, 88, 91, 92, 94, 96, 99, 100, 103, 105, 106, 109, 111, 112, 115, 116, 118, 120, 124, 126, 129

Offset: 1

Author

Ryan Bresler, Jan 01 2022

Keywords

• nonn

Comments

a(n) is prime only when n is the greater of a twin prime pair (A006512). All other terms are composite.

Examples

			9 is a term because the previous prime < 9 is 7, and 9 - 7 = 2, which is prime.
		

Crossrefs

Cf. A175090, A006512.

Programs

Mathematica

Select[Range[2, 130], PrimeQ[# - NextPrime[#, -1]] &] (* Amiram Eldar, Jan 02 2022 *)

PARI

isok(k) = if (k>2, my(q=precprime(k-1)); isprime(k-q)); \\ Michel Marcus, Jan 02 2022

Python

from sympy import isprime, prevprime
def ok(n): return n > 2 and isprime(n-prevprime(n))
print([k for k in range(249) if ok(k)]) # Michael S. Branicky, Jan 01 2022