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A376380 Products of 5 distinct primes that are sandwiched between twin prime numbers.

%I A376380 #18 Jan 11 2025 16:25:52
%S A376380 2310,2730,6090,6270,7590,8970,9282,13398,14322,15330,17490,19470,
%T A376380 21318,22110,23370,27690,28182,29670,30090,32190,32370,32718,32802,
%U A376380 32970,33330,37590,40530,41610,45318,46830,47058,48678,48990,49170,49530,49938,51198,52710,56238,56910,57270,58110,58170,59010,60762
%N A376380 Products of 5 distinct primes that are sandwiched between twin prime numbers.
%C A376380 All terms are even.
%C A376380 All terms are of the form 6r, where r is coprime to 6, so they all are Zumkeller numbers (A083207). - _Ivan N. Ianakiev_, Sep 24 2024
%H A376380 Charles R Greathouse IV, <a href="/A376380/b376380.txt">Table of n, a(n) for n = 1..10000</a>
%e A376380 2310 is in the sequence a term because 2310=2*3*5*7*11 is the product of five distinct primes and 2309, 2311 are a couple of twin primes.
%e A376380 2730 is in the sequence a term because 2730=2*3*5*7*13 is the product of five distinct primes and 2729, 2731 are a couple of twin primes.
%p A376380 ispenta:= proc(n) local F;
%p A376380   F:= ifactors(n)[2];
%p A376380   nops(F) = 5 and F[..,2] = [1$5]
%p A376380 end proc:
%p A376380 select(t -> isprime(t-1) and isprime(t+1) and ispenta(t), [seq(i,i=6 .. 10^5,12)]); # _Robert Israel_, Sep 24 2024
%t A376380 Select[Range[6, 61000, 6], And @@ PrimeQ[# + {-1, 1}] && FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1} &] (* _Amiram Eldar_, Sep 22 2024 *)
%o A376380 (PARI) list(lim)=my(v=List()); forprime(p=11,lim\210, my(P=lim\(6*p)); forprime(q=7,min(P\5,p-2), my(Q=P\q); forprime(r=5,min(Q,q-2), my(t=6*p*q*r); if(isprime(t+1) && isprime(t-1), listput(v,t))))); Set(v) \\ _Charles R Greathouse IV_, Sep 24 2024
%Y A376380 Intersection of A014574 and A046387.
%Y A376380 Cf. A353022.
%K A376380 nonn
%O A376380 1,1
%A A376380 _Massimo Kofler_, Sep 22 2024