A234103 Products p*q*r of distinct primes for which (p*q*r + 1)/2 is prime.

105, 165, 273, 345, 357, 385, 465, 561, 705, 777, 861, 885, 897, 957, 1005, 1045, 1113, 1173, 1185, 1281, 1353, 1545, 1645, 1653, 1677, 1705, 1905, 1965, 2037, 2065, 2121, 2185, 2193, 2233, 2301, 2373, 2445, 2553, 2613, 2865, 2877, 2905, 2985, 3021, 3157

Offset: 1

Author

Clark Kimberling, Dec 27 2013

Keywords

• nonn
• easy

Examples

			105 = 3*5*7, and (105 + 1)/2 is prime.
		

Crossrefs

Cf. A234100, A234102, A234104.

Programs

Mathematica

t = Select[Range[1, 10000, 2], Map[Last, FactorInteger[#]] == Table[1, {3}] &]; Take[(t + 1)/2, 120] (* A234102 *)
v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A234103 *)
(w + 1)/2  (* A234104 *)    (* Peter J. C. Moses, Dec 23 2013 *)
With[{nn=50},Select[Union[Select[Times@@@Subsets[Prime[Range[2,nn]],{3}],PrimeQ[(#+1)/2]&]],#<=15*Prime[nn]&]]  (* Harvey P. Dale, May 12 2025 *)