A098855 Numbers n such that 4^n + 2^n - 1 is prime.

1, 2, 3, 4, 6, 10, 16, 24, 26, 35, 52, 55, 95, 144, 379, 484, 939, 1284, 1300, 2651, 3644, 3979, 7179, 8304, 14840, 32040, 47759, 57279

Offset

1,2

Comments

Or, numbers n such that (2^n+1)*2^n-1 is prime.

Links

Table of n, a(n) for n=1..28.

F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1

Formula

A110082(n)=2^(a(n)-1)*(4^a(n)+2^a(n)-1).

Example

1300 is in the sequence because 4^1300+2^1300-1 is prime.
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.
4^4+2^4-1 = 271 prime so a(4)=4.

Mathematica

Do[If[PrimeQ[4^m+2^m-1], Print[m]], {m, 8000}] - Farideh Firoozbakht, Aug 03 2005

Prog

PFGW64 from primeform group and SCRIPTIFY
Command : PFGW64 -f in.txt
in.txt file :
SCRIPT
DIM nn, 0
DIMS tt
OPENFILEOUT myfile, a(n).txt
LABEL loopn
SET nn, nn+1
SETS tt, %d\,; nn
PRP 4^nn+2^nn-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopn
LABEL a
WRITE myfile, tt
GOTO loopn -- Pierre CAMI, May 10 2012
(PARI) is(n)=ispseudoprime(4^n+2^n-1) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A110079, A110082, A210733.

Sequence in context: A364587 A221996 A070542 * A143283 A104767 A072944

Adjacent sequences: A098852 A098853 A098854 * A098856 A098857 A098858

Keyword

nonn

Author

Pierre CAMI, Oct 11 2004

Extensions

Corrected by Torin Huzil (thuzil(AT)gmail.com), Sep 15 2005

More terms from Pierre CAMI, May 10 2012

Status

approved