A207572 Least number k > 0 such that 3*prime(n)*2^k-1 is a prime number.

1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 4, 1, 4, 7, 2, 8, 4, 2, 3, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 5, 5, 15, 3, 11, 1, 1, 2, 3, 1, 1, 3, 1, 3, 2, 2, 3, 1, 2, 2, 2, 1, 8, 6, 10, 1, 1, 4, 3, 1, 5, 4, 1, 3, 1, 1, 1, 1, 1, 3, 12, 6, 2, 2, 3, 1, 1

Offset

1,5

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

3*2*2^1-1 = 11 prime so a(1)=1.
3*3*2^1-1 = 17 prime so a(2)=1.
3*5*2^1-1 = 29 prime so a(3)=1.
3*7*2^1-1 = 41 prime so a(4)=1.
3*11*2^1-1 = 65 composite.
3*11*2^2-1 = 131 prime so a(5)=2.

Mathematica

Table[p = Prime[n]; k = 1; While[! PrimeQ[3*p*2^k - 1], k++]; k, {n, 100}] (* 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
WRITE myfile, tt
GOTO loopn

Crossrefs

Sequence in context: A347380 A308638 A356320 * A289623 A086195 A086197

Adjacent sequences: A207569 A207570 A207571 * A207573 A207574 A207575

Keyword

nonn

Author

Pierre CAMI, Feb 20 2012

Status

approved