Some properties of a special set of recurring sequences

Hugh C. Williams

Vol. 77 (1978), No. 1, 273–285

DOI: 10.2140/pjm.1978.77.273

Abstract

Several number theoretic and identity properties of three special second order recurring sequences are established. These are used to develop a necessary and sufficient condition for any integer of the form 2ⁿ3^mA− 1 (A < 2ⁿ⁺¹3^m − 1) to be prime. This condition can be easily implemented on a computer.

Mathematical Subject Classification

Primary: 10A25, 10A25

Secondary: 10-04

Milestones

Received: 29 March 1977

Revised: 21 November 1977

Published: 1 July 1978