A242131 Smallest k such that (2*k*3^n-1)*2*k*3^n+1 is prime, with k not divisible by 3.

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, 26, 16, 35, 104, 13, 11, 61, 5, 68, 98, 26, 220, 113, 43, 10, 11, 13, 127, 29, 14, 4, 8, 142, 29, 76, 151, 73, 13, 100, 287, 47, 16, 26, 158, 163, 35, 152, 26

Offset

1,3

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

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, A242132, A242133.

Sequence in context: A344026 A133866 A356045 * A177266 A356124 A272534

Adjacent sequences: A242128 A242129 A242130 * A242132 A242133 A242134

Keyword

nonn

Author

Pierre CAMI, May 05 2014

Status

approved