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

%I A080892 #39 Jan 16 2024 11:15:00
%S A080892 3,8,10,12,13,15,16,19,20,21,25,28,39,42,44,48,55,57,60,66,67,76,78,
%T A080892 85,118,130,156,162,193,212,214,217,218,228,244,312,330,352,357,376,
%U A080892 386,388,412,442,449,464,480,525,545,552,630,644
%N A080892 Numbers k such that 3^k-2 is a semiprime.
%C A080892 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
%H A080892 Herman Jamke and others, <a href="/A080892/a080892.txt">Illustration of first 42 terms</a>
%H A080892 Ryan Propper, <a href="http://cs.stanford.edu/people/rpropper/math/factors/3n-2.txt">Table of factorizations of 3^n - 2.</a>
%H A080892 Factordb.com, <a href="http://factordb.com/index.php?query=3%5E658+-+2">Status of 3^658-2</a>.
%e A080892 a(1) = 3 because 3^3-2 = 25 = 5*5.
%e A080892 a(2) = 8 because 3^8-2 = 6559 = 7*937.
%e A080892 a(3) = 10 because 3^10-2 = 59047 = 137*431.
%t A080892 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 *)
%o A080892 (PARI) for(n=1,200,if(bigomega(3^n-2)==2,print1(n","))) /* Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 02 2007 */
%Y A080892 Cf. A001358, A014224, A014232, A080798.
%K A080892 more,nonn
%O A080892 1,1
%A A080892 _Hugo Pfoertner_, Mar 30 2003
%E A080892 Added missing a(1)=3 by Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 01 2007
%E A080892 a(27)-a(42) from Herman Jamke (hermanjamke(AT)fastmail.fm) and _Ryan Propper_, Apr 01, Apr 19 2007, May 11 2007
%E A080892 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)
%E A080892 a(43)-a(47) from _Sean A. Irvine_, Jun 13 2012
%E A080892 a(48) from _Ryan Propper_, Sep 30 2012
%E A080892 a(49)-a(52) from _Ryan Propper_, Feb 07 2013