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A242175
Numbers n such that n*2^n + 1 is a semiprime.
3
2, 3, 4, 5, 8, 9, 11, 16, 21, 33, 35, 101, 105, 131, 158, 165, 191, 234, 251, 435, 453, 459, 561, 579, 604, 671, 744, 753, 933, 963, 1041, 1146, 1168, 1254
OFFSET
1,1
COMMENTS
The semiprimes of this form are 9, 25, 65, 161, 2049, 4609, 22529, ... (A242116).
a(35) >= 1528. Below 2000, 1794 and 1961 are in the sequence. Unknown factorization for 1528, 1576, 1908. - Hugo Pfoertner, Jul 29 2019
FORMULA
A002064(a(n)) = A242116(n). - Amiram Eldar, Nov 27 2019
MATHEMATICA
Select[Range[165], Plus@@Last/@FactorInteger[# * 2^# + 1]==2&]
PROG
(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
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Vincenzo Librandi, May 07 2014
EXTENSIONS
a(17) from Bruno Berselli, May 08 2014
a(18)-a(30) from Luke March, Aug 13 2015
a(31)-a(34) from Hugo Pfoertner, Jul 29 2019
Wrong term 941 removed by Amiram Eldar, Nov 27 2019
STATUS
approved