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

2310, 2730, 6090, 6270, 7590, 8970, 9282, 13398, 14322, 15330, 17490, 19470, 21318, 22110, 23370, 27690, 28182, 29670, 30090, 32190, 32370, 32718, 32802, 32970, 33330, 37590, 40530, 41610, 45318, 46830, 47058, 48678, 48990, 49170, 49530, 49938, 51198, 52710, 56238, 56910, 57270, 58110, 58170, 59010, 60762

Offset: 1

Author

Massimo Kofler, Sep 22 2024

Keywords

• nonn

Comments

All terms are even.

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

Examples

			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.
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.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A014574 and A046387.

Cf. A353022.

Programs

Maple

ispenta:= proc(n) local F;
  F:= ifactors(n)[2];
  nops(F) = 5 and F[..,2] = [1$5]
end proc:
select(t -> isprime(t-1) and isprime(t+1) and ispenta(t), [seq(i,i=6 .. 10^5,12)]); # Robert Israel, Sep 24 2024

Mathematica

Select[Range[6, 61000, 6], And @@ PrimeQ[# + {-1, 1}] && FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1} &] (* Amiram Eldar, Sep 22 2024 *)

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