A164518 Primes of the form A162143(k) + 2.

11027, 65027, 74531, 119027, 184043, 308027, 314723, 370883, 423803, 603731, 783227, 804611, 815411, 915851, 938963, 1238771, 1279163, 1461683, 1490843, 1535123, 1550027, 1718723, 2556803, 2673227, 2812331, 3059003, 3493163

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 14 2009

Keywords

• nonn

Comments

Primes of the form 2 + q^2*r^2*s^2 where q, r, and s are three distinct primes.

Examples

			a(1) = 11027 = A000040(1337) = A162143(7) + 2.
		

Links

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

Crossrefs

Cf. A056899, A162143, A164517.

Programs

Maple

N:= 10^7: # to get all terms <= N
P:= select(isprime, [seq(i,i=3..floor(sqrt(N-2)/15))]):
R:= NULL:
for i from 1 to nops(P) do
  for j from 1 to i-1 while (3*P[i]*P[j])^2<=N-2 do
    for k from 1 to j-1 do
      p:= (P[i]*P[j]*P[k])^2+2;
      if p > N then break fi;
      if isprime(p) then R:= R, p fi
od od od:
sort([R]); # Robert Israel, Jun 05 2018

Mathematica

f[n_]:=FactorInteger[n][[1,2]]==2&&Length[FactorInteger[n]]==3&&FactorInteger[n][[2, 2]]==2&&FactorInteger[n][[3,2]]==2; lst={};Do[p=Prime[n];If[f[p-2], AppendTo[lst,p]],{n,4,9!}];lst
With[{nn=30},Take[Union[Select[Times@@(#^2)+2&/@Subsets[Prime[ Range[ nn]], {3}],PrimeQ]],nn]] (* Harvey P. Dale, Mar 14 2016 *)

Extensions

Edited by R. J. Mathar, Aug 21 2009