A234104 - OEIS

%I #12 Jan 29 2023 14:56:28

%S 53,83,137,173,179,193,233,281,353,389,431,443,449,479,503,523,557,

%T 587,593,641,677,773,823,827,839,853,953,983,1019,1033,1061,1093,1097,

%U 1117,1151,1187,1223,1277,1307,1433,1439,1453,1493,1511,1579,1583,1601,1619

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

%H Robert Israel, <a href="/A234104/b234104.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n) local s;

%p   if not isprime(n) then return false fi;

%p   s:= ifactors(2*n-1)[2];

%p   nops(s)=3 and map(t -> t[2],s)=[1,1,1]

%p end proc:

%p select(filter, [seq(i,i=3..1619,2)]); # _Robert Israel_, May 11 2020

%t t = Select[Range[1, 10000, 2], Map[Last, FactorInteger[#]] == Table[1, {3}] &]; Take[(t + 1)/2, 120] (* A234102 *)

%t v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A234103 *)

%t (w + 1)/2  (* A234104 *)    (* _Peter J. C. Moses_, Dec 23 2013 *)

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

%Y Cf. A234102, A234103, A234101.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Dec 27 2013