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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A007304, A051634, A363167, A364738.

Sequence in context: A124410 A211775 A346177 * A116894 A124629 A222696

Adjacent sequences: A363779 A363780 A363781 * A363783 A363784 A363785

Keyword

nonn

Author

Massimo Kofler, Jun 21 2023

Extensions

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

Status

approved