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integer sequences
   
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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 ...