

A210733


Least k > n1 such that 4^n + 2^k  1 is a prime number.


2



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
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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+2^11=5 prime so a(1)=1.
4^2+2^21=19 prime so a(2)=2.
4^3+2^31=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, nn1
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; kk
PRP 4^nn+2^kk1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
WRITE myfile, tt
GOTO loopn


CROSSREFS

Sequence in context: A317491 A028335 A007464 * A265564 A064764 A123131
Adjacent sequences: A210730 A210731 A210732 * A210734 A210735 A210736


KEYWORD

nonn


AUTHOR

Pierre CAMI, May 10 2012


EXTENSIONS

Missing a(2103) inserted into bfile by Andrew Howroyd, Feb 24 2018


STATUS

approved



