A080892 Numbers k such that 3^k-2 is a semiprime.

3, 8, 10, 12, 13, 15, 16, 19, 20, 21, 25, 28, 39, 42, 44, 48, 55, 57, 60, 66, 67, 76, 78, 85, 118, 130, 156, 162, 193, 212, 214, 217, 218, 228, 244, 312, 330, 352, 357, 376, 386, 388, 412, 442, 449, 464, 480, 525, 545, 552, 630, 644

Offset

1,1

Comments

The next roadblock to being able to extend the sequence is 3^658 - 2, a 314-decimal digit composite with no known factors. - Ryan Propper, Feb 07 2013

Links

Table of n, a(n) for n=1..52.

Herman Jamke and others, Illustration of first 42 terms

Ryan Propper, Table of factorizations of 3^n - 2.

Factordb.com, Status of 3^658-2.

Example

a(1) = 3 because 3^3-2 = 25 = 5*5.
a(2) = 8 because 3^8-2 = 6559 = 7*937.
a(3) = 10 because 3^10-2 = 59047 = 137*431.

Mathematica

Do[f = 3^n - 2; If[ !PrimeQ[f], s = FactorIntegerECM[f]; If[PrimeQ[s] && PrimeQ[f/s], Print[n]]], {n, 2, 10^3}] (* Ryan Propper, May 11 2007 *)

Prog

(PARI) for(n=1, 200, if(bigomega(3^n-2)==2, print1(n", "))) /* Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 02 2007 */

Crossrefs

Cf. A001358, A014224, A014232, A080798.

Sequence in context: A176118 A151693 A007284 * A177091 A347690 A246589

Adjacent sequences: A080889 A080890 A080891 * A080893 A080894 A080895

Keyword

more,nonn

Author

Hugo Pfoertner, Mar 30 2003

Extensions

Added missing a(1)=3 by Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 01 2007

a(27)-a(42) from Herman Jamke (hermanjamke(AT)fastmail.fm) and Ryan Propper, Apr 01, Apr 19 2007, May 11 2007

Restored missing terms < 388 by Sean A. Irvine, Apr 06 2011 (Some correctly stated terms in Jamke's and Propper's list had been omitted during editing)

a(43)-a(47) from Sean A. Irvine, Jun 13 2012

a(48) from Ryan Propper, Sep 30 2012

a(49)-a(52) from Ryan Propper, Feb 07 2013

Status

approved