cp's OEIS Frontend

A242175 Numbers k such that k*2^k + 1 is a semiprime.

%I A242175 #42 Mar 19 2025 10:24:01
%S A242175 2,3,4,5,8,9,11,16,21,33,35,101,105,131,158,165,191,234,251,435,453,
%T A242175 459,561,579,604,671,744,753,933,963,1041,1146,1168,1254,1794
%N A242175 Numbers k such that k*2^k + 1 is a semiprime.
%C A242175 The semiprimes of this form are 9, 25, 65, 161, 2049, 4609, 22529, ... (A242116).
%C A242175 a(35) >= 1528. Below 2000, 1794 and 1961 are in the sequence. Unknown factorization for 1528, 1576, 1908. - _Hugo Pfoertner_, Jul 29 2019
%C A242175 The k*2^k + 1 corresponding to 1528 and 1576 each have at least three prime factors. - _Tyler Busby_, Mar 16 2025
%H A242175 FactorDB, <a href="http://factordb.com/index.php?query=1908*2%5E1908%2B1">Status of 1908*2^1908+1</a>.
%F A242175 A002064(a(n)) = A242116(n). - _Amiram Eldar_, Nov 27 2019
%t A242175 Select[Range[165], Plus@@Last/@FactorInteger[# * 2^# + 1]==2&]
%o A242175 (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..230] | IsSemiprime(s) where s is n*2^n+1]; // _Bruno Berselli_, May 08 2014
%Y A242175 Cf. A001358, A002064, A005849, A242116, A242273.
%K A242175 nonn,more,hard
%O A242175 1,1
%A A242175 _Vincenzo Librandi_, May 07 2014
%E A242175 a(17) from _Bruno Berselli_, May 08 2014
%E A242175 a(18)-a(30) from _Luke March_, Aug 13 2015
%E A242175 a(31)-a(34) from _Hugo Pfoertner_, Jul 29 2019
%E A242175 Wrong term 941 removed by _Amiram Eldar_, Nov 27 2019
%E A242175 a(35) from _Tyler Busby_, Mar 16 2025