# Prime-Generating Recurrence

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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.

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Contributed by: Eric Rowland (July 2008)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This recurrence was discovered at the 2003 NKS Summer School (*NKS|Online*) 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.

## Permanent Citation