A234104 Primes of the form (p*q*r + 1)/2, where p, q, r are distinct primes.

53, 83, 137, 173, 179, 193, 233, 281, 353, 389, 431, 443, 449, 479, 503, 523, 557, 587, 593, 641, 677, 773, 823, 827, 839, 853, 953, 983, 1019, 1033, 1061, 1093, 1097, 1117, 1151, 1187, 1223, 1277, 1307, 1433, 1439, 1453, 1493, 1511, 1579, 1583, 1601, 1619

Offset: 1

Author

Clark Kimberling, Dec 27 2013

Keywords

• nonn
• easy

Examples

			(3*5*7 + 1)/2 = 53.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A234102, A234103, A234101.

Programs

Maple

filter:= proc(n) local s;
  if not isprime(n) then return false fi;
  s:= ifactors(2*n-1)[2];
  nops(s)=3 and map(t -> t[2],s)=[1,1,1]
end proc:
select(filter, [seq(i,i=3..1619,2)]); # Robert Israel, May 11 2020

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 *)
Module[{nn=100},Select[(Times@@#+1)/2&/@Subsets[Prime[Range[nn]],{3}],PrimeQ[ #] && #<=5*Prime[nn]&]]//Union (* Harvey P. Dale, Jan 29 2023 *)