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, 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

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