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

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, 1794

Offset: 1

Author

Vincenzo Librandi, May 07 2014

Keywords

• nonn
• more
• hard

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

The k*2^k + 1 corresponding to 1528 and 1576 each have at least three prime factors. - Tyler Busby, Mar 16 2025

Links

• FactorDB, Status of 1908*2^1908+1.

Crossrefs

Cf. A001358, A002064, A005849, A242116, A242273.

Programs

Magma

IsSemiprime:=func; [n: n in [2..230] | IsSemiprime(s) where s is n*2^n+1]; // Bruno Berselli, May 08 2014

Mathematica

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

Formula

A002064(a(n)) = A242116(n). - Amiram Eldar, Nov 27 2019

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

a(35) from Tyler Busby, Mar 16 2025