login
Smallest k such that (2*k*3^n-1)*2*k*3^n+1 is prime, with k not divisible by 3.
4

%I #19 Apr 25 2016 11:50:02

%S 1,1,4,1,5,7,7,8,4,1,14,7,13,5,11,22,5,7,28,8,7,8,44,4,13,8,11,4,5,52,

%T 26,16,35,104,13,11,61,5,68,98,26,220,113,43,10,11,13,127,29,14,4,8,

%U 142,29,76,151,73,13,100,287,47,16,26,158,163,35,152,26

%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="/A242131/b242131.txt">Table of n, a(n) for n = 1..4000</a>

%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, A242132, A242133.

%K nonn

%O 1,3

%A _Pierre CAMI_, May 05 2014