# Simple Somos Sequence Calculator

An old Russian olympiad problem asked to prove that the sequence generated by the following algorithm

a_{1} = 1, a_{2} = 1,

a_{n} = (a_{n-1}^{2} + 2) / a_{n-2}, n ≥ 3.

consists entirely of positive integers.

A proof of this fact can be found on a separate page, where it was also observed that the statement holds when 2 in the numerator is replaced with any positive integer m. The applet below generates as many members of the sequence as fit the applet drawing area. This is a spreadsheet and you can modify the entry B1, that carries the value of m, manually.

- Step into the Elliptic Realm
- Simple Somos Sequence - a Russian Olympiad problem
- Simple Somos Sequence Calculator

- The Rascal Triangle
- Frieze Patterns

|Activities| |Contact| |Front page| |Contents|

Copyright © 1996-2018 Alexander Bogomolny68394521