A363782 Products of three distinct strong primes.

5423, 6919, 7667, 11033, 11803, 12529, 13079, 13277, 14773, 16687, 18139, 18241, 18821, 18887, 20009, 20213, 21373, 22649, 23749, 24013, 25201, 25619, 25789, 26609, 27269, 27863, 28897, 29087, 30217, 30481, 30943, 32021, 32153, 32219, 33031, 33473, 34133, 35003, 35629, 35717, 36839

Offset: 1

Author

Massimo Kofler, Jun 21 2023

Keywords

• nonn

Comments

Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.

Examples

			5423 = 11*17*29 and 11 > (7+13)/2, 17 > (13+19)/2, 29 > (23+31)/2.
6919 = 11*17*37 and 11 > (7+13)/2, 17 > (13+19)/2, 37 > (31+41)/2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A007304, A051634, A363167, A364738.

Programs

Mathematica

strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 37000, 2], (f = FactorInteger[#])[[;; , 2]] == {1, 1, 1} && AllTrue[f[[;; , 1]], strongQ] &] (* Amiram Eldar, Jun 21 2023 *)
Module[{nn=50,strgpr},strgpr=Select[Partition[Prime[Range[nn]],3,1],#[[2]]>(#[[1]]+#[[3]])/2&][[;;,2]];Take[Union[Times@@@Subsets[strgpr,{3}]],nn]] (* Harvey P. Dale, Aug 21 2024 *)

Extensions

Definition clarified by N. J. A. Sloane, Oct 08 2023