The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #24 Sep 08 2022 08:46:08
%S 3,5,11,12,18,20,21,24,25,35,43,45,53,58,61,71,73,75,123,124,140,147,
%T 157,205,208,233,243,245,293,301
%N Numbers n such that n*6^n+1 is semiprime.
%C The semiprimes of this form are: 649, 38881, 3990767617, 26121388033, 1828079220031489, 73123168801259521, 460675963447934977,...
%C 464 is definitely in this sequence, however 436 may or may not be. - _Carl Schildkraut_, Aug 28 2015
%C A continuation in the range 302 ... 1000 would use all terms without "?" and potentially ?-marked terms corresponding to composites with unknown factorization: 436?, 464, 511?, 512, 613, 662?, 720, 730, 802?, 865?, 943. - _Hugo Pfoertner_, Aug 05 2019
%H factordb.com, <a href="http://factordb.com/index.php?query=436*6%5E436%2B1">Status of 436*6^436+1</a>.
%t Select[Range[435], PrimeOmega[# 6^# + 1] == 2 &]
%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..435] | IsSemiprime(s) where s is n*6^n+1];
%o (PARI) is(n)=bigomega(n*6^n+1)==2 \\ _Anders Hellström_, Aug 28 2015
%Y Cf. similar sequences listed in A242203.
%Y Cf. A050917, A242176.
%K nonn,more,hard
%O 1,1
%A _Vincenzo Librandi_, May 10 2014
%E a(19)-a(30) from _Carl Schildkraut_, Aug 28 2015