

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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


LINKS

Table of n, a(n) for n=1..34.
FactorDB, Status of 1528*2^1528+1.


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

Cf. A001358, A002064, A005849, A242116, A242273.
Sequence in context: A044051 A083132 A302602 * A325662 A275771 A118956
Adjacent sequences: A242172 A242173 A242174 * A242176 A242177 A242178


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



