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Products of two distinct strong primes.
1

%I #10 Oct 08 2023 09:45:46

%S 121,187,289,319,407,451,493,629,649,697,737,781,841,869,1003,1067,

%T 1073,1111,1139,1177,1189,1207,1343,1369,1397,1507,1517,1639,1649,

%U 1681,1711,1717,1793,1819,1943,1969,2059,2101,2159,2167,2183,2291,2329,2419,2453,2479,2497,2533,2627,2629,2747

%N Products of two distinct strong primes.

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

%e 121 = 11^2 and 11 > (7+13)/2.

%e 187 = 11*17 and 11 > (7+13)/2, 17 > (13+19)/2.

%e 493 = 17*29 and 17 > (13+19)/2, 29 > (23+31)/2.

%t strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 3000, 2], MemberQ[{{1, 1}, {2}}, (f = FactorInteger[#])[[;; , 2]]] && AllTrue[f[[;; , 1]], strongQ] &] (* _Amiram Eldar_, Aug 07 2023 *)

%Y Cf. A001358, A051634, A363167, A363782.

%K nonn

%O 1,1

%A _Massimo Kofler_, Aug 07 2023

%E Definition clarified by _N. J. A. Sloane_, Oct 08 2023