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

1,1

Links

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

Example

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

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 *)

Crossrefs

Cf. A234102, A234103, A234101.

Sequence in context: A136065 A354915 A234102 * A212420 A001836 A144939

Adjacent sequences: A234101 A234102 A234103 * A234105 A234106 A234107

Keyword

nonn,easy

Author

Clark Kimberling, Dec 27 2013

Status

approved