Proth Number

A Proth number is a number of the form  for odd ,  a positive integer, and . The  condition is needed since otherwise, every odd number  would be a Proth number. The first few Proth numbers are 3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, ... (OEIS A080075).

The Cullen numbers are a special case of the Proth numbers with  (and the inequality restriction dropped). The Fermat numbers are a special case of the Proth numbers with .

REFERENCES:

McNamara, J. and Mills, M. "Factoring of Proth Numbers." http://www.fidn.org/proth1.html.

Sloane, N. J. A. Sequence A080075 in "The On-Line Encyclopedia of Integer Sequences."