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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

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Last modified May 12 09:53 EDT 2021. Contains 343821 sequences. (Running on oeis4.)