Pell number

A number in the sequence created from the recurrence relation






The first few Pell numbersMathworldPlanetmath are 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, listed in A000129 of Sloane’s OEIS.

A Pell number for any given index can also be calculated from earlier Pell numbers with


The formula


works too. From this particular formula it can be deduced that the sequence of Pell numbers can be used in a continued fractionDlmfMathworldPlanetmath of the square root of 2MathworldPlanetmath as well as the silver ratio.

Yet another way to calculate Pell numbers is by squaring the terms of Pascal’s triangle and adding up the antidiagonals. Arranging the Markov numbersMathworldPlanetmath in a binary graph tree and reading the numbers on 2’s branch gives the Pell numbers with odd indices.

Only Pell numbers with prime indexes can also be prime. This fact is used in some tests for pseudoprimality.

Title Pell number
Canonical name PellNumber
Date of creation 2013-03-22 15:46:44
Last modified on 2013-03-22 15:46:44
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 6
Author CompositeFan (12809)
Entry type Definition
Classification msc 11B39
Defines Pell number