A378097 Products of 6 distinct primes that are sandwiched between twin prime numbers.

43890, 51870, 84630, 102102, 140070, 149730, 153510, 168630, 224070, 251790, 269178, 281190, 308490, 316470, 317730, 322770, 355110, 376530, 381990, 383838, 389298, 404430, 432390, 434010, 459030, 467670, 486330, 487830, 496230, 506730, 520410, 531570, 545790, 552090, 560490, 573342, 576030, 583338

Offset

1,1

Comments

All the terms are divisible by 6.

Links

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

Example

43890 is in the sequence a term because 43890=2*3*5*7*11*19 is the product of six distinct primes and 43889, 43891 are a couple of twin primes.
51870 is in the sequence a term because 51870=2*3*5*7*13*19 is the product of six distinct primes and 51869, 51871 are a couple of twin primes.

Maple

with(priqueue):
initialize(pq):
insert([-2*3*5*7*11*13, 2, 2, 3, 5, 7, 11, 13], pq);
R:= NULL: count:= 0:
while count < 100 do
  t:= extract(pq);
  x:= -t[1];
  if isprime(x-1) and isprime(x+1) then
    count:= count+1; R:= R, x
  fi;
  for i from t[2] to 5 do
    p:= nextprime(t[8]);
    insert ([t[1] * p/t[i+3], i, seq(t[j], j=3..i+2), seq(t[j], j=i+4..8), p], pq);
  od;
od:
R; # Robert Israel, Nov 16 2025

Mathematica

Select[6 * Range[10^5], PrimeQ[#-1] && PrimeQ[#+1] && FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1, 1} &] (* Amiram Eldar, Nov 16 2024 *)

Crossrefs

Intersection of A014574 and A067885.

Cf. A083207 (supersequence), A353022, A376380.

Sequence in context: A037147 A043303 A233790 * A359127 A391448 A223457

Adjacent sequences: A378094 A378095 A378096 * A378098 A378099 A378100

Keyword

nonn

Author

Massimo Kofler, Nov 16 2024

Status

approved