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

Author

Massimo Kofler, Apr 26 2023

Keywords

• nonn

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1914

Crossrefs

Cf. A000040, A046386, A140078 and A362578.

Programs

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 *)