A362630 Squarefree semiprimes (products of two distinct primes) whose factors are strong primes.
187, 319, 407, 451, 493, 629, 649, 697, 737, 781, 869, 1003, 1067, 1073, 1111, 1139, 1177, 1189, 1207, 1343, 1397, 1507, 1517, 1639, 1649, 1711, 1717, 1793, 1819, 1943, 1969, 2059, 2101, 2159, 2167, 2183, 2291, 2329, 2419, 2453, 2479, 2497, 2533, 2627, 2629, 2747, 2761, 2771, 2813, 2911, 2923, 2929, 2959
Offset: 1
Keywords
Examples
187 = 11*17 and 11 > (7+13)/2, 17 > (13+19)/2. 319 = 11*29 and 11 > (7+13)/2, 29 > (23+31)/2.
Programs
-
Mathematica
strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 3000, 2], (f = FactorInteger[#])[[;; , 2]] == {1, 1} && AllTrue[f[[;; , 1]], strongQ] &] (* Amiram Eldar, Jun 21 2023 *)
Comments