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%I #11 Jun 05 2018 22:34:38
%S 11027,65027,74531,119027,184043,308027,314723,370883,423803,603731,
%T 783227,804611,815411,915851,938963,1238771,1279163,1461683,1490843,
%U 1535123,1550027,1718723,2556803,2673227,2812331,3059003,3493163
%N Primes of the form A162143(k) + 2.
%C Primes of the form 2 + q^2*r^2*s^2 where q, r, and s are three distinct primes.
%H Robert Israel, <a href="/A164518/b164518.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 11027 = A000040(1337) = A162143(7) + 2.
%p N:= 10^7: # to get all terms <= N
%p P:= select(isprime, [seq(i,i=3..floor(sqrt(N-2)/15))]):
%p R:= NULL:
%p for i from 1 to nops(P) do
%p for j from 1 to i-1 while (3*P[i]*P[j])^2<=N-2 do
%p for k from 1 to j-1 do
%p p:= (P[i]*P[j]*P[k])^2+2;
%p if p > N then break fi;
%p if isprime(p) then R:= R, p fi
%p od od od:
%p sort([R]); # _Robert Israel_, Jun 05 2018
%t 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
%t With[{nn=30},Take[Union[Select[Times@@(#^2)+2&/@Subsets[Prime[ Range[ nn]], {3}],PrimeQ]],nn]] (* _Harvey P. Dale_, Mar 14 2016 *)
%Y Cf. A056899, A162143, A164517.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Aug 14 2009
%E Edited by _R. J. Mathar_, Aug 21 2009
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