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A376380
Products of 5 distinct primes (or pentaprimes) that are sandwiched between twin prime numbers.
1
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
1,1
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
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
Intersection of A014574 and A046387.
Cf. A353022.
Sequence in context: A051270 A046387 A136154 * A258360 A076252 A264718
KEYWORD
nonn
AUTHOR
Massimo Kofler, Sep 22 2024
STATUS
approved