A242132 Smallest k such that (2*k*3^n+1)*2*k*3^n-1 is prime, with k not divisible by 3.

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, 20, 38, 1, 5, 11, 1, 14, 22, 10, 31, 2, 35, 8, 107, 112, 103, 80, 22, 40, 104, 20, 1, 29, 40, 1, 61, 77, 8, 41, 62, 1, 5, 46, 20, 35, 29, 68, 23, 85, 49, 58, 23

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[{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 *)

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, A242133.

Sequence in context: A176439 A048834 A010504 * A011450 A231015 A183031

Adjacent sequences: A242129 A242130 A242131 * A242133 A242134 A242135

Keyword

nonn

Author

Pierre CAMI, May 05 2014

Status

approved