cp's OEIS Frontend

A164521 Primes of the form A162142(k) - 2.

%I A164521 #15 Jun 05 2018 22:34:52
%S A164521 3373,753569,2146687,3048623,6539201,8120599,10218311,17373977,
%T A164521 18609623,19034161,32461757,44738873,59776469,69426529,72511711,
%U A164521 77854481,88121123,116930167,133432829,299418307,338608871,413493623,458314009,679151437
%N A164521 Primes of the form A162142(k) - 2.
%C A164521 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.
%H A164521 Robert Israel, <a href="/A164521/b164521.txt">Table of n, a(n) for n = 1..10000</a>
%e A164521 3373 + 2 = 3375 = 3^3*5^3. 753569 + 1 = 753571 = 7^3*13^3.
%p A164521 N:= 10^10: # to get all terms <= N
%p A164521 P:= select(isprime, [seq(i,i=3..floor((N+2)^(1/3)/3))]):
%p A164521 R:= NULL:
%p A164521 for i from 1 to nops(P) do
%p A164521     for j from 1 to i-1 do
%p A164521       p:= (P[i]*P[j])^3-2;
%p A164521       if p > N then break fi;
%p A164521       if isprime(p) then R:= R, p fi
%p A164521 od od:
%p A164521 sort([R]); # _Robert Israel_, Jun 05 2018
%t A164521 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
%t A164521 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 *)
%Y A164521 Cf. A006881, A056899, A144953, A162142, A164517, A164518, A164519, A164520.
%K A164521 nonn
%O A164521 1,1
%A A164521 _Vladimir Joseph Stephan Orlovsky_, Aug 14 2009
%E A164521 Edited and examples corrected by _R. J. Mathar_, Aug 21 2009