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%I #52 Oct 07 2023 03:00:19
%S 4,5,8,12,20,24,25,28,32,38,42,44,60,62,66,70,72,80,122,125,148,228,
%T 244,270,389,390,432,464,470,488,549,560,804,862
%N Numbers k such that k*3^k - 1 is semiprime.
%C The semiprimes of this form are 323, 1214, 52487, 6377291, 69735688019, 6778308875543, 21182215236074, 640550188738907, 59296646043258911, ...
%C 804 is a term of this sequence. - _Luke March_, Aug 22 2015
%C The smallest unresolved value of k is now 862. - _Sean A. Irvine_, Jun 20 2022
%C The smallest unresolved value of k is now 866. - _Tyler Busby_, Oct 06 2023
%C From _Jon E. Schoenfield_, Oct 06 2023: (Start)
%C After the possible term 866, the only remaining 3-digit terms are 912 and 984, unless 920 is a term.
%C If k is an odd term, then k*3^k - 1 is even, so (k*3^k - 1)/2 is a prime. The next odd terms after 549 are 1125 and 12889. Odd terms are in A366323. (End)
%t Select[Range[241], PrimeOmega[# 3^# - 1]==2&]
%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..241] | IsSemiprime(s) where s is n*3^n-1];
%o (PARI) isok(n)=bigomega(n*3^n-1)==2 /* _Anders Hellström_, Aug 18 2015 */
%Y Cf. similar sequence listed in A242273.
%Y Cf. A006553, A060352, A366323.
%K nonn,more
%O 1,1
%A _Vincenzo Librandi_, May 12 2014
%E a(21)-a(23) from _Carl Schildkraut_, Aug 18 2015
%E a(24)-a(32) from _Luke March_, Aug 22 2015
%E a(32) = 804 removed by _Sean A. Irvine_, Apr 25 2022
%E a(32)-a(33) from _Sean A. Irvine_, Jun 20 2022
%E a(34) from _Tyler Busby_, Oct 06 2023
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