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.
Full version: pdf,
(Concerned with sequences
Received July 6 2018; revised versions received October 1 2018; October 3 2018.
Published in Journal of Integer Sequences, December 5 2018.
Journal of Integer Sequences home page