A361796 Prime numbers preceded by two consecutive numbers which are products of four distinct primes (or tetraprimes).

8647, 15107, 20407, 20771, 21491, 23003, 23531, 24767, 24971, 27967, 29147, 33287, 34847, 36779, 42187, 42407, 42667, 43331, 43991, 46807, 46867, 51431, 52691, 52747, 53891, 54167, 58567, 63247, 63367, 69379, 71711, 73607, 73867, 74167, 76507, 76631, 76847, 80447, 83591, 84247, 86243

Offset

1,1

Links

Table of n, a(n) for n=1..41.

Example

8647 (prime), 8646 = 2*3*11*131 and 8645 = 5*7*13*19.
15107 (prime), 15106 = 2*7*13*83 and 15105 = 3*5*19*53.
20407 (prime), 20406 = 2*3*19*179 and 20405 = 5*7*11*53.

Maple

N:= 10^5: # for terms <= N
TP:= NULL:
P:= select(isprime, [2, seq(i, i=3..N/30, 2)]):
for i from 1 to nops(P) do
  for j from 1 to i-1 while P[i]*P[j] <= N/6 do
    for k from 1 to j-1 while P[i]*P[j]*P[k] <= N/2 do
      TP:= TP, op(select(`<=`, map(`*`, P[1..k-1], P[i]*P[j]*P[k]), N));
od od od:
TP:= {TP}:
TTP:= TP intersect map(`-`, TP, 1):
sort(convert(select(isprime, map(`+`, TTP, 2)), list)); # Robert Israel, Apr 28 2023

Mathematica

q[n_] := FactorInteger[n][[;; , 2]] == {1, 1, 1, 1}; Select[Prime[Range[10^4]], AllTrue[# - {1, 2}, q] &] (* Amiram Eldar, Apr 26 2023 *)

Crossrefs

Cf. A000040, A046386, A140078 and A362578.

Sequence in context: A190467 A057658 A075006 * A031591 A031771 A205732

Adjacent sequences: A361793 A361794 A361795 * A361797 A361798 A361799

Keyword

nonn

Author

Massimo Kofler, Apr 26 2023

Status

approved