In mathematics, the Pell numbers and companion Pell numbers (Pell-Lucas numbers) are both sequences of integers. Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... In mathematics, a sequence is a list of objects (or events) arranged in a linear fashion, such that the order of the members is well defined and significant. ... The integers consist of the positive natural numbers (1, 2, 3, …) the negative natural numbers (−1, −2, −3, ...) and the number zero. ...

Pell numbers

The Pell numbers are defined recursively by: In mathematics and computer science, recursion is a particular way of specifying (or constructing) a class of objects (or an object from a certain class) with the help of a reference to other objects of the class: a recursive definition defines objects in terms of the already defined objects of...

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 (sequence A000129 in OEIS): 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378... The On-Line Encyclopedia of Integer Sequences (OEIS) is an extensive searchable database of integer sequences, freely available on the Web. ... 0 (zero) is both a number — or, more precisely, a numeral representing a number — and a numerical digit. ... Look up one in Wiktionary, the free dictionary. ... 2 (two) is a number, numeral, and glyph. ... Look up five in Wiktionary, the free dictionary. ... 12 (twelve) is the natural number following 11 and preceding 13. ... 29 (twenty-nine) is the natural number following 28 and preceding 30. ... 70 (seventy) is the natural number following 69 and preceding 71. ... 169 is the natural number following one hundred sixty-eight and preceding one hundred seventy. ...

Pell prime

A Pell prime is a Pell number that is prime. The first few Pell primes are In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors. ...

2, 5, 29, 5741, ….

Pell square

A Pell square is a Pell number that is square. The first few Pell squares are A square as a geometric shape is described and illustrated at square (geometry). ...

0, 1, 169, ….

Companion Pell numbers (Pell-Lucas numbers)

The Companion Pell numbers are defined recursively by: A Sierpinski triangle —a confined recursion of triangles to form a geometric lattice. ...

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 (sequence A002203 in OEIS): 2, 2, 6, 14, 34, 82, 198, 478... The On-Line Encyclopedia of Integer Sequences (OEIS) is an extensive searchable database of integer sequences, freely available on the Web. ... 2 (two) is a number, numeral, and glyph. ... 2 (two) is a number, numeral, and glyph. ... Number 6, in this article, refers to the mathematical number. ... 14 (fourteen) is the natural number following 13 and preceding 15. ... 34 (thirty-four) is the natural number following 33 and preceding 35. ... 82 is the natural number following 81 and preceding 83. ... 198 is the natural number between 197 and 199. ...