A242133 - OEIS

%I #12 Jul 11 2014 15:20:29

%S 1,5,1,1,5,7,1,13,2,1,1,7,37,5,1,5,16,68,28,82,17,40,5,5,44,17,2,26,8,

%T 13,25,13,31,35,65,61,28,23,7,35,43,49,64,5,29,29,95,26,4,68,7,29,49,

%U 46,37,14,29,1,166,20,23,47,52,106,2,4,197,14,133,29

%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="/A242133/b242133.txt">Table of n, a(n) for n = 1..4000</a>

%t sk[n_]:=Module[{c=3^n,k=1},While[!PrimeQ[(2*k*c+1)2*k*c+1] || Divisible[ k,3], k++];k]; Array[sk,70] (* _Harvey P. Dale_, Jul 11 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

%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, A242132.

%K nonn

%O 1,2

%A _Pierre CAMI_, May 05 2014