A229927 Smallest k >= n such that (4^n-1)*2^k - 1 is prime.

1, 2, 3, 4, 8, 6, 7, 13, 11, 16, 103, 12, 16, 52, 26, 16, 26, 34, 38, 28, 23, 22, 26, 24, 50, 41, 30, 28, 32, 46, 31, 34, 202, 34, 35, 40, 47, 113, 46, 50, 44, 54, 58, 46, 51, 48, 130, 59, 64, 101, 60, 62, 94, 74, 88, 98, 71, 234, 67, 93, 83, 101, 308, 64, 92

Offset

1,2

Comments

Conjecture: there is no "Riesel" number of the form 4^n-1; that is, a(n) exists for all n.

Links

Pierre CAMI, Table of n, a(n) for n = 1..2500

Example

(4^1-1)*2^1-1=5 prime so a(1)=1.
(4^2-1)*2^2-1=59 prime so a(2)=2.

Mathematica

sk[n_]:=Module[{k=n, c=4^n-1}, While[!PrimeQ[c*2^k-1], k++]; k]; Array[sk, 70] (* Harvey P. Dale, Jul 30 2020 *)

Prog

PFGW & SCRIPTIFY
SCRIPT
DIM k
DIM n, 0
DIMS tt
OPENFILEOUT myf, a(n).txt
LABEL a
SET n, n+1
IF n>2500 THEN END
SET k, n-1
LABEL b
SET k, k+1
SETS tt, %d, %d\,; n; k
PRP (4^n-1)*2^k-1, tt
IF ISPRP THEN GOTO c
GOTO b
LABEL c
WRITE myf, tt
GOTO a

Crossrefs

Cf. A098845.

Sequence in context: A123494 A123716 A329717 * A222256 A367870 A223540

Adjacent sequences: A229924 A229925 A229926 * A229928 A229929 A229930

Keyword

nonn

Author

Pierre CAMI, Oct 03 2013

Status

approved