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Numbers n which are a product of two primes j and k such that n+j-k and n-j+k are both primes.
5

%I #8 Aug 08 2016 01:31:55

%S 6,10,15,22,57,85,87,142,187,217,235,267,274,295,339,382,505,565,579,

%T 589,667,694,799,835,849,862,889,922,1059,1111,1159,1317,1339,1555,

%U 1569,1797,1969,1977,2122,2182,2217,2227,2229,2245,2319,2335,2359,2497,2577

%N Numbers n which are a product of two primes j and k such that n+j-k and n-j+k are both primes.

%C In other words, numbers n which are a product of two distinct primes a and b such that n+-d are primes, where d is the difference between a and b.

%e a(10)=217 because 217 has only one pair of prime factors (7 and 31) and both 217+7-31 and 217-7+31 (193 and 241) are primes.

%t pdpQ[{a_,b_}]:=Module[{d=b-a},AllTrue[a*b+{d,-d},PrimeQ]]; With[{upto = 2600}, Select[ Times@@@Select[Subsets[Prime[Range[upto/2]],{2}],pdpQ]// Union, #<=upto&]] (* _Harvey P. Dale_, Aug 02 2016 *)

%Y Cf. A001358.

%K nonn

%O 1,1

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