Simple Somos Sequence Calculator

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

   a₁ = 1, a₂ = 1,
   a_n = (a_n-1² + 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. The parameter m ranges from 2 through 100.

• Step into the Elliptic Realm
• Simple Somos Sequence - a Russian Olympiad problem
  • Simple Somos Sequence Calculator
• The Rascal Triangle
• Frieze Patterns

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