A242133 Smallest k such that (2*k*3^n+1)*2*k*3^n+1 is prime, with k not divisible by 3.

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

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