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%I #22 Apr 25 2016 11:50:02
%S 1,2,1,2,14,2,8,5,4,5,4,40,5,29,5,7,5,19,13,1,37,34,13,2,1,17,13,2,7,
%T 28,34,26,61,2,41,43,2,10,118,52,4,4,11,7,20,139,35,11,4,29,40,8,44,7,
%U 64,37,47,175,14,23,142,23,5,32,104,110,4,26,47,25
%N Smallest k such that (2*k*3^n-1)*2*k*3^n-1 is prime, with k not divisible by 3.
%C Conjectures: the ratio a(n)/n is always <10 and sum(a(n)/n)/N for n=1 to N tends to 1 as N tends to infinity.
%H Pierre CAMI, <a href="/A242085/b242085.txt">Table of n, a(n) for n = 1..4000</a>
%e (1*2*3^1-1)*1*2*3^1-1=29 so a(1)=1.
%e (1*2*3^2-1)*1*2*3^2-1=305 composite, (2*2*3^2-1)*2*2*3^2-1=1259 prime so a(2)=2.
%t sk[n_]:=Module[{k=1,c=2*3^n},While[Divisible[k,3]||!PrimeQ[(k*c-1) (k*c)-1],k++];k]; Array[sk,70] (* _Harvey P. Dale_, Aug 05 2014 *)
%o (PFGW & SCRIPT)
%o SCRIPT
%o DIM n,0
%o DIM i
%o DIM pp
%o DIMS t
%o OPENFILEOUT myf,a(n).txt
%o LABEL loop1
%o SET n,n+1
%o SET i,0
%o LABEL loop2
%o SET i,i+1
%o SETS t,%d,%d\,;n;i
%o SET pp,(2*i*3^n-1)*2*i*3^n-1
%o PRP pp,t
%o IF ISPRP THEN GOTO a
%o GOTO loop2
%o LABEL a
%o WRITE myf,t
%o GOTO loop1
%Y Cf. A242131, A242132, A242133.
%K nonn
%O 1,2
%A _Pierre CAMI_, May 04 2014
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