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# Prime-Generating Recurrence

This Demonstration explores solutions of the recurrence through the difference sequence , which exhibits complex behavior. For the initial condition , the sequence consists entirely of s and primes, making this recurrence a rare "naturally occurring" generator of primes.
This result is not true in general: for example, letting produces , and letting produces . However, for these initial conditions, the difference sequence eventually consists entirely of s and primes. It is an unsolved problem to determine whether all initial conditions eventually produce only s and primes.
You can choose to view all terms of the difference sequence or only the terms which are not .

### DETAILS

This recurrence was discovered at the 2003 NKS Summer School by a group led by Matt Frank.
This Demonstration allows initial conditions . For , is for .
For more information, see E. S. Rowland, "A Natural Prime-Generating Recurrence," Journal of Integer Sequences [online], 11(2), 2008.

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