OFFSET
1,1
COMMENTS
One of the three primes must be 2. - Robert Israel, Apr 09 2019
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
110=2*5*11; 2^2+5^2+11^2=150+-1 -> primes
MAPLE
N:= 10000: # to get terms <= N
P:= select(isprime, [seq(i, i=5..N/10, 2)]): nP:= nops(P):
Res:= NULL:
for i from 1 to nP do
a:= P[i];
for j from i+1 to nP do
b:= P[j];
if 2*a*b > N then break fi;
q:= 4+a^2 + b^2;
if isprime(q-1) and isprime(q+1) then Res:= Res, 2*a*b; fi;
od
od:
sort([Res]); # Robert Israel, Apr 09 2019
MATHEMATICA
l[n_]:=Last/@FactorInteger[n]; f[n_]:=First/@FactorInteger[n]; lst={}; Do[If[l[n]=={1, 1, 1}, a=f[n][[1]]; b=f[n][[2]]; c=f[n][[3]]; If[PrimeQ[a^2+b^2+c^2-1]&&PrimeQ[a^2+b^2+c^2+1], AppendTo[lst, n]]], {n, 8!}]; lst
With[{nn=2000}, Select[Union[2Times@@#&/@Select[Subsets[Prime[Range[2, nn]], {2}], AllTrue[Total[#^2]+4+{1, -1}, PrimeQ]&]], #<=6nn&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 20 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Apr 27 2010
STATUS
approved