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

%I A369957 #10 Apr 05 2025 11:07:04
%S A369957 47,73,113,127,151,167,233,239,241,313,409,431,433,439,521,593,599,
%T A369957 601,607,719,727,967,1031,1087,1249,1409,1439,1471,1559,1601,1831,
%U A369957 1913,1993,2089,2161,2273,2281,2287,2311,2351,2393,2633,2689,2711,2729,2767,2833,2879,3079,3313,3319,3359,3511
%N A369957 Primes p such that p - 3 and p + 3 are triprimes.
%C A369957 Primes p such that p - 3 and p + 3 each have 3 prime factors, counted with multiplicity.
%C A369957 Primes p such that one of p - 3 and p + 3 is 4 times a prime and the other is 2 times a semiprime.
%H A369957 Robert Israel, <a href="/A369957/b369957.txt">Table of n, a(n) for n = 1..10000</a>
%e A369957 a(3) = 113 is a term because 113 is prime, and 110 = 2 * 5 * 11 and 116 = 2^2 * 29 are triprimes.
%p A369957 filter:= proc(n)
%p A369957   isprime(n) and numtheory:-bigomega(n-3) = 3 and numtheory:-bigomega(n+3) = 3
%p A369957 end proc:
%p A369957 select(filter, [seq(i,i=3..20000,2)]);
%t A369957 s = {}; p = 5; Do[If[{3, 3} == PrimeOmega[{p - 3, p + 3}],
%t A369957 AppendTo[s, p]]; p = NextPrime[p], {500}]; s
%t A369957 Select[Prime[Range[500]],PrimeOmega[#-3]==PrimeOmega[#+3]==3&]
%Y A369957 Cf. A001222, A014612, A063643.
%K A369957 nonn
%O A369957 1,1
%A A369957 _Zak Seidov_ and _Robert Israel_, Feb 07 2024