A164521 - OEIS

%I #15 Jun 05 2018 22:34:52

%S 3373,753569,2146687,3048623,6539201,8120599,10218311,17373977,

%T 18609623,19034161,32461757,44738873,59776469,69426529,72511711,

%U 77854481,88121123,116930167,133432829,299418307,338608871,413493623,458314009,679151437

%N Primes of the form A162142(k) - 2.

%C 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 Robert Israel, <a href="/A164521/b164521.txt">Table of n, a(n) for n = 1..10000</a>

%e 3373 + 2 = 3375 = 3^3*5^3. 753569 + 1 = 753571 = 7^3*13^3.

%p N:= 10^10: # to get all terms <= N

%p P:= select(isprime, [seq(i,i=3..floor((N+2)^(1/3)/3))]):

%p R:= NULL:

%p for i from 1 to nops(P) do

%p     for j from 1 to i-1 do

%p       p:= (P[i]*P[j])^3-2;

%p       if p > N then break fi;

%p       if isprime(p) then R:= R, p fi

%p od od:

%p sort([R]); # _Robert Israel_, Jun 05 2018

%t 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 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 Cf. A006881, A056899, A144953, A162142, A164517, A164518, A164519, A164520.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Aug 14 2009

%E Edited and examples corrected by _R. J. Mathar_, Aug 21 2009