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A242175 Numbers n such that n*2^n + 1 is a semiprime. 3

%I

%S 2,3,4,5,8,9,11,16,21,33,35,101,105,131,158,165,191,234,251,435,453,

%T 459,561,579,604,671,744,753,933,963,1041,1146,1168,1254

%N Numbers n such that n*2^n + 1 is a semiprime.

%C The semiprimes of this form are 9, 25, 65, 161, 2049, 4609, 22529, ... (A242116).

%C a(35) >= 1528. Below 2000, 1794 and 1961 are in the sequence. Unknown factorization for 1528, 1576, 1908. - _Hugo Pfoertner_, Jul 29 2019

%H FactorDB, <a href="http://factordb.com/index.php?query=1528*2%5E1528%2B1">Status of 1528*2^1528+1</a>.

%F A002064(a(n)) = A242116(n). - _Amiram Eldar_, Nov 27 2019

%t Select[Range[165], Plus@@Last/@FactorInteger[# * 2^# + 1]==2&]

%o (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 Cf. A001358, A002064, A005849, A242116, A242273.

%K nonn,more,hard

%O 1,1

%A _Vincenzo Librandi_, May 07 2014

%E a(17) from _Bruno Berselli_, May 08 2014

%E a(18)-a(30) from _Luke March_, Aug 13 2015

%E a(31)-a(34) from _Hugo Pfoertner_, Jul 29 2019

%E Wrong term 941 removed by _Amiram Eldar_, Nov 27 2019

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Last modified July 9 11:58 EDT 2020. Contains 335543 sequences. (Running on oeis4.)