A234100 Products p*q*r of distinct primes for which (p*q*r - 1)/2 is prime.

195, 255, 399, 455, 483, 555, 615, 627, 663, 759, 795, 915, 935, 1095, 1235, 1239, 1295, 1419, 1455, 1479, 1515, 1547, 1595, 1659, 1767, 1955, 2067, 2139, 2235, 2247, 2343, 2387, 2555, 2595, 2607, 2639, 2847, 2895, 2919, 2967, 3219, 3243, 3335, 3395, 3399

Offset: 1

Author

Clark Kimberling, Dec 27 2013

Keywords

• nonn
• easy

Examples

			97 = (3*5*13 - 1)/2, and 3*5*13 is the least product p*q*r of 3 distinct primes for which (p*q*r - 1)/2 is prime, so a(1) = 3*5*13.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..274 (all terms up to 20000)

Crossrefs

Cf. A234099, A234101, A234093, A234102.

Programs

Mathematica

t = Select[Range[1, 10000, 2], Map[Last, FactorInteger[#]] == Table[1, {3}] &]; Take[(t - 1)/2, 120] (* A234099 *)
v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* this sequence *)
(w - 1)/2 (* A234101 *)    (* Peter J. C. Moses, Dec 23 2013 *)
With[{upto=4000},Select[Union[Times@@@Select[Subsets[Prime[ Range[ PrimePi[ upto/ 6]]],{3}],PrimeQ[(Times@@#-1)/2]&]],#<=upto&]] (* Harvey P. Dale, May 12 2017 *)