|Ivars Peterson's MathTrek| October 27, 1997 Recreational
mathematics furnishes a vast playing field for amateur and
professional mathematicians alike. It combines a sense of play
with the joy of discovery. Sometimes the results are
mathematically trivial; occasionally they lead to new
mathematical insights. Whole numbers or integers are often the
subject of such pursuits. Once someone discovers an interesting
pattern or type of behavior, those particular numbers are likely
to earn a collective name. So we have perfect numbers, amicable
numbers, lucky numbers, Mersenne numbers, Fermat numbers,
Fibonacci numbers, Keith numbers, Niven numbers, Carmichael
numbers, Stirling numbers, Catalan numbers, Ruth-Aaron numbers,
Rhonda numbers, and so on. The list keeps growing! One such
curiosity came about in 1982 as the result of a telephone call.
When phoning his brother-in-law, mathematician Albert Wilansky
of Lehigh University in Bethlehem, Penn., noticed that the
telephone number had a striking property. The number,