A210733 Least k > n-1 such that 4^n + 2^k - 1 is a prime number.

1, 2, 3, 4, 6, 6, 12, 9, 10, 10, 27, 13, 15, 22, 16, 16, 18, 19, 39, 22, 22, 43, 24, 24, 48, 26, 28, 43, 32, 38, 75, 33, 36, 58, 35, 57, 55, 47, 48, 52, 54, 72, 52, 51, 72, 54, 72, 53, 64, 62, 52, 52, 63, 60, 55, 60, 316, 70, 63, 68, 64, 96, 66, 115, 66, 92

Offset

1,2

Comments

As n increases k is on average 1.43*n.

Links

Pierre CAMI, Table of n, a(n) for n = 1..3867

Example

4^1+2^1-1=5 prime so a(1)=1.
4^2+2^2-1=19 prime so a(2)=2.
4^3+2^3-1=71 prime so a(3)=3.

Mathematica

Table[k = n; While[! PrimeQ[4^n + 2^k - 1], k++];  k, {n, 100}] (* T. D. Noe, May 16 2012 *)

Prog

(PFGW64 and SCRIPTIFY)
Command : PFGW64 -f in.txt
in.txt file :
SCRIPT
DIM nn, 0
DIM kk
DIMS tt
OPENFILEOUT myfile, a(n).txt
LABEL loopn
SET nn, nn+1
SET kk, nn-1
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; kk
PRP 4^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: A028335 A346117 A007464 * A265564 A064764 A340267

Adjacent sequences: A210730 A210731 A210732 * A210734 A210735 A210736

Keyword

nonn

Author

Pierre CAMI, May 10 2012

Extensions

Missing a(2103) inserted into b-file by Andrew Howroyd, Feb 24 2018

Status

approved