OFFSET

1,1

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.

LINKS

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

EXAMPLE

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

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

CROSSREFS

KEYWORD

nonn

AUTHOR

Zak Seidov and Robert Israel, Feb 07 2024

STATUS

approved