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Iterations of the Words-to-Numbers Function
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Matthew E. Coppenbarger

School of Mathematical Sciences

85 Lomb Memorial Drive

Rochester Institute of Technology

Rochester, NY 14623-5603

USA

**Abstract:**

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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