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

3373, 753569, 2146687, 3048623, 6539201, 8120599, 10218311, 17373977, 18609623, 19034161, 32461757, 44738873, 59776469, 69426529, 72511711, 77854481, 88121123, 116930167, 133432829, 299418307, 338608871, 413493623, 458314009, 679151437

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 14 2009

Keywords

• nonn

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.

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

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 *)

Extensions

Edited and examples corrected by R. J. Mathar, Aug 21 2009