Journal of Integer Sequences, Vol. 21 (2018), Article 18.9.2

Iterations of the Words-to-Numbers Function

Matthew E. Coppenbarger
School of Mathematical Sciences
85 Lomb Memorial Drive
Rochester Institute of Technology
Rochester, NY 14623-5603


The Words-to-Numbers function takes a nonnegative integer and maps it to the number of characters required to spell the number in English. For each k = 0, 1, ... , 8, we determine the minimal nonnegative integer n such that the iterates of n converge to the fixed point (through the Words-to-Numbers function) in exactly k iterations. Our travels take us from some simple answers, to an etymology of the names of large numbers, to Conway/Guy's established system representing the name of any integer, and finally use generating functions to arrive at a very large number.

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(Concerned with sequences A001273 A005589 A227290 A301408.)

Received July 6 2018; revised versions received October 1 2018; October 3 2018. Published in Journal of Integer Sequences, December 5 2018.

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