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Numbers m that are a product of two primes j and k such that m+j+k is prime.
4

%I #19 Feb 24 2024 01:07:44

%S 6,10,14,15,21,26,33,34,35,38,46,51,55,57,58,65,74,85,86,93,111,118,

%T 123,141,143,145,155,158,161,166,177,178,185,194,201,203,205,206,209,

%U 215,221,254,267,278,295,298,319,321,323,326,327,329,334,341,346,355,365

%N Numbers m that are a product of two primes j and k such that m+j+k is prime.

%H Harvey P. Dale, <a href="/A088709/b088709.txt">Table of n, a(n) for n = 1..1000</a>

%e a(2)=10 because 10 has only one pair of prime factors (2 and 5) and 10 + 2 + 5 = 17, which is prime.

%t ptpQ[n_]:=Module[{fi=FactorInteger[n]},Length[fi]==2&&Union[ fi[[All,2]]] == {1}&&PrimeQ[n+Total[fi[[All,1]]]]]; Select[Range[400],ptpQ] (* _Harvey P. Dale_, Nov 06 2020 *)

%Y Cf. A001358.

%K nonn

%O 1,1

%A Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 11 2003