A393795 7-smooth numbers that are averages of twin prime pairs.

4, 6, 12, 18, 30, 42, 60, 72, 108, 150, 180, 192, 240, 270, 420, 432, 600, 810, 882, 1050, 1152, 1620, 2268, 2592, 2688, 3000, 3360, 3528, 4050, 4800, 5880, 6300, 7350, 7560, 8232, 8820, 9000, 9720, 10500, 15360, 18522, 21600, 23040, 26250, 26880, 28350, 29400, 30870, 33600, 33750, 35280, 49392

Offset

1,1

Links

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

Example

a(5) = 30 is a term because 30 = 2*3*5 has no prime factors > 7 and 30 is the average of the twin primes 29 and 31.

Maple

N:= 100: # for a(1) .. a(N)
V:= Vector(N): V[1]:= 4: count:= 1: with(priqueue):
initialize(pq);
insert([-6, 0, 0, 0, 0], pq);
while count < N do
  t:= extract(pq);
  x:= -t[1];
  if isprime(x+1) and isprime(x-1) then count:= count+1; V[count]:= x fi;
  insert([-7*x, t[2], t[3], t[4], t[5]+1], pq);
  if t[5]=0 then
    insert([-5*x, t[2], t[3], t[4]+1, 0], pq);
    if t[4] = 0 then
      insert([-3*x, t[2], t[3]+1, 0, 0], pq);
      if t[3] = 0 then
        insert([-2*x, t[2]+1, 0, 0, 0], pq);
  fi fi fi;
od:
convert(V, list);

Mathematica

Select[Range[50000], AllTrue[First/@FactorInteger[#], #<=7&]&&PrimeQ[#+1]&&PrimeQ[#-1]&] (* James C. McMahon, Feb 28 2026 *)

Crossrefs

Intersection of A002473 and A014574.

Sequence in context: A217259 A014574 A258838 * A377067 A383650 A384530

Adjacent sequences: A393792 A393793 A393794 * A393796 A393797 A393798

Keyword

nonn

Author

Robert Israel, Feb 27 2026

Status

approved