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A208281 Numbers n such that 3*prime(n)*2^k - 1 is prime for some k > 0 and then 3*prime(n)*2^k + 1 is also prime. 1
1, 2, 3, 4, 6, 7, 9, 15, 24, 27, 28, 33, 34, 35, 58, 60, 61, 65, 67, 68, 69, 74, 78, 81, 86, 91, 92, 96, 105, 106, 108, 110, 119, 121, 125, 128, 129, 133, 134, 135, 137, 138, 146, 155, 172, 173, 174, 177, 179, 187, 199, 215, 216, 224 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Note that only first k for which 3*prime(n)*2^k - 1 is prime is used to test whether 3*prime(n)*2^k + 1 is prime.

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..6836

EXAMPLE

3*prime(1)*2^1-1=11 prime,13 prime so a(1)=1

3*prime(2)*2^1-1=17 prime,19 prime so a(2)=2

3*prime(3)*2^1-1=29 prime,31 prime so a(3)=3

3*prime(4)*2^1-1=41 prime,43 prime so a(4)=4

3*prime(5)*2^1-1=65 composite

3*prime(5)*2^2-1=131 prime,133 composite

3*prime(6)*2^1-1=77 composite

3*prime(6)*2^2-1=155 composite

3*prime(6)*2^3-1=311 prime,313 prime so a(5)=6

MATHEMATICA

t = {}; Do[p = Prime[n]; k = 1; While[! PrimeQ[3*p*2^k - 1], k++]; If[PrimeQ[3*p*2^k + 1], AppendTo[t, n]], {n, 224}]; t (* T. D. Noe, Feb 29 2012 *)

PROG

PFGW64 from Primeform group and SCRIPTIFY

Command pfgw64 -f in.txt

in.txt file :

SCRIPT

DIM nn, 0

DIM kk

DIMS tt

OPENFILEOUT myfile, k.txt

LABEL loopn

SET nn, nn+1

IF nn>50000 THEN END

SET kk, 0

LABEL loopk

SET kk, kk+1

SETS tt, %d, %d\,; nn; kk

PRP 3*p(nn)*2^kk-1, tt

IF ISPRP THEN GOTO a

IF ISPRIME THEN GOTO a

GOTO loopk

LABEL a

PRP 3*p(nn)*2^kk+1, tt

IF ISPRP THEN GOTO b

IF ISPRIME THEN GOTO b

GOTO loopn

LABEL b

WRITE myfile, tt

GOTO loopn

CROSSREFS

Cf. A207572.

Sequence in context: A064414 A224482 A002475 * A306074 A250252 A246274

Adjacent sequences:  A208278 A208279 A208280 * A208282 A208283 A208284

KEYWORD

nonn

AUTHOR

Pierre CAMI, Feb 25 2012

STATUS

approved

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Last modified December 2 20:25 EST 2021. Contains 349445 sequences. (Running on oeis4.)