Pell number

In mathematics, the Pell numbers and Companion Pell Numbers (Pell-Lucas Numbers) are both sequences of integers.

Pell numbers

The Pell numbers are defined recursively by:

P_n=\begin{cases}0&\mbox{if }n=0;\\1&\mbox{if }n=1;\\2P_{n-1}+P_{n-2}&\mbox{otherwise.}\end{cases}

In words: you start with 0 and 1, and then produce the next Pell number by adding twice the previous Pell number to the Pell number before that. The first few terms of the sequence are : , 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378...

Pell prime

A Pell prime is a Pell number that is prime. The first few Pell primes are

2, 5, 29, 5741, ….

Companion Pell numbers (Pell-Lucas numbers)

The Companion Pell numbers are defined recursively by:

P_n=\begin{cases}2&\mbox{if }n=0;\\2&\mbox{if }n=1;\\2P_{n-1}+P_{n-2}&\mbox{otherwise.}\end{cases}

In words: you start with 2 and 2, and then produce the next Pell number by adding twice the previous Pell number to the Pell number before that. The first few terms of the sequence are : 2, 2, 6, 14, 34, 82, 198, 478... Integer sequences

Pell-Folge | Nombre de Pell

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Pell numbers

Pell prime

Companion Pell numbers (Pell-Lucas numbers)