%I #15 Mar 04 2023 13:04:32
%S 1,7,1,4,1,8,11,5,20,1,16,10,1,8,2,5,5,5,2,50,20,128,11,13,23,5,52,2,
%T 20,38,1,5,11,1,14,22,10,31,2,35,8,107,112,103,80,22,40,104,20,1,29,
%U 40,1,61,77,8,41,62,1,5,46,20,35,29,68,23,85,49,58,23
%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="/A242132/b242132.txt">Table of n, a(n) for n = 1..4000</a>
%t sk[n_]:=Module[{k=1},While[Mod[k,3]==0||!PrimeQ[(2k 3^n+1)2 k 3^n-1],k++]; k]; Array[sk,70] (* _Harvey P. Dale_, Mar 04 2023 *)
%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
%o (PARI) a(n) = {k = 1; while (! isprime((2*k*3^n+1)*2*k*3^n-1) || !(k % 3), k++); k;} \\ _Michel Marcus_, May 05 2014
%Y Cf. A242085, A242131, A242133.
%K nonn
%O 1,2
%A _Pierre CAMI_, May 05 2014