

A242133


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


4



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, 13, 25, 13, 31, 35, 65, 61, 28, 23, 7, 35, 43, 49, 64, 5, 29, 29, 95, 26, 4, 68, 7, 29, 49, 46, 37, 14, 29, 1, 166, 20, 23, 47, 52, 106, 2, 4, 197, 14, 133, 29
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

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.


LINKS

Pierre CAMI, Table of n, a(n) for n = 1..4000


MATHEMATICA

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 *)


PROG

(PFGW & SCRIPT )
SCRIPT
DIM n, 0
DIM i
DIM pp
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET n, n+1
SET i, 0
LABEL loop2
SET i, i+1
SETS t, %d, %d\,; n; i
SET pp, (2*i*3^n+1)*2*i*3^n+1
PRP pp, t
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
WRITE myf, t
GOTO loop1
(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


CROSSREFS

Cf. A242085, A242131, A242132.
Sequence in context: A046607 A152717 A071856 * A144221 A209575 A159570
Adjacent sequences: A242130 A242131 A242132 * A242134 A242135 A242136


KEYWORD

nonn


AUTHOR

Pierre CAMI, May 05 2014


STATUS

approved



