A369957 Primes p such that p - 3 and p + 3 are triprimes.

47, 73, 113, 127, 151, 167, 233, 239, 241, 313, 409, 431, 433, 439, 521, 593, 599, 601, 607, 719, 727, 967, 1031, 1087, 1249, 1409, 1439, 1471, 1559, 1601, 1831, 1913, 1993, 2089, 2161, 2273, 2281, 2287, 2311, 2351, 2393, 2633, 2689, 2711, 2729, 2767, 2833, 2879, 3079, 3313, 3319, 3359, 3511

Offset: 1

Author

Zak Seidov and Robert Israel, Feb 07 2024

Keywords

• nonn

Comments

Primes p such that p - 3 and p + 3 each have 3 prime factors, counted with multiplicity.

Primes p such that one of p - 3 and p + 3 is 4 times a prime and the other is 2 times a semiprime.

Examples

			a(3) = 113 is a term because 113 is prime, and 110 = 2 * 5 * 11 and 116 = 2^2 * 29 are triprimes.
		

Links

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

Crossrefs

Cf. A001222, A014612, A063643.

Programs

Maple

filter:= proc(n)
  isprime(n) and numtheory:-bigomega(n-3) = 3 and numtheory:-bigomega(n+3) = 3
end proc:
select(filter, [seq(i,i=3..20000,2)]);

Mathematica

s = {}; p = 5; Do[If[{3, 3} == PrimeOmega[{p - 3, p + 3}],
AppendTo[s, p]]; p = NextPrime[p], {500}]; s
Select[Prime[Range[500]],PrimeOmega[#-3]==PrimeOmega[#+3]==3&]