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