OFFSET
1,1
COMMENTS
Primes p such that p+2 is the cube of a squarefree semiprime, i.e., such that p+2 = q^3*r^3 where q and r are two distinct primes.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
3373 + 2 = 3375 = 3^3*5^3. 753569 + 1 = 753571 = 7^3*13^3.
MAPLE
N:= 10^10: # to get all terms <= N
P:= select(isprime, [seq(i, i=3..floor((N+2)^(1/3)/3))]):
R:= NULL:
for i from 1 to nops(P) do
for j from 1 to i-1 do
p:= (P[i]*P[j])^3-2;
if p > N then break fi;
if isprime(p) then R:= R, p fi
od od:
sort([R]); # Robert Israel, Jun 05 2018
MATHEMATICA
f3[n_]:=FactorInteger[n][[1, 2]]==3&&Length[FactorInteger[n]]==2&&FactorInteger[n][[2, 2]]==3; lst={}; Do[p=Prime[n]; If[f3[p+2], AppendTo[lst, p]], {n, 4, 4*9!}]; lst
csfsQ[n_]:=Module[{c=Surd[n+2, 3]}, SquareFreeQ[c]&&PrimeOmega[c]==2]; Select[Prime[Range[353*10^5]], csfsQ] (* Harvey P. Dale, Jan 07 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Aug 14 2009
EXTENSIONS
Edited and examples corrected by R. J. Mathar, Aug 21 2009
STATUS
approved