A242085 Smallest k such that (2*k*3^n-1)*2*k*3^n-1 is prime, with k not divisible by 3.

1, 2, 1, 2, 14, 2, 8, 5, 4, 5, 4, 40, 5, 29, 5, 7, 5, 19, 13, 1, 37, 34, 13, 2, 1, 17, 13, 2, 7, 28, 34, 26, 61, 2, 41, 43, 2, 10, 118, 52, 4, 4, 11, 7, 20, 139, 35, 11, 4, 29, 40, 8, 44, 7, 64, 37, 47, 175, 14, 23, 142, 23, 5, 32, 104, 110, 4, 26, 47, 25

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

Example

(1*2*3^1-1)*1*2*3^1-1=29 so a(1)=1.
(1*2*3^2-1)*1*2*3^2-1=305 composite, (2*2*3^2-1)*2*2*3^2-1=1259 prime so a(2)=2.

Mathematica

sk[n_]:=Module[{k=1, c=2*3^n}, While[Divisible[k, 3]||!PrimeQ[(k*c-1) (k*c)-1], k++]; k]; Array[sk, 70] (* Harvey P. Dale, Aug 05 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

Crossrefs

Cf. A242131, A242132, A242133.

Sequence in context: A153908 A048296 A016542 * A007402 A334505 A375955

Adjacent sequences: A242082 A242083 A242084 * A242086 A242087 A242088

Keyword

nonn

Author

Pierre CAMI, May 04 2014

Status

approved