USAP PAETE

adedios

Names for Numbers
Ivars Peterson
29 July 2006

Recreational mathematics offers 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 numbers that are perfect, amicable, lucky, narcissistic, weird, and so on. Many of these names also commemorate people: Mersenne, Fermat, Fibonacci, Keith, Niven, Carmichael, Stirling, Catalan, Ruth-Aaron, Rhonda. And 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 noticed that the telephone number had a striking property.

The number, 493-7775 (4,937,775), is composite, meaning that it can be expressed as the product of prime numbers: 3 x 5 x 5 x 65,837. Interestingly, when the digits of the original number are added together, the result (42) equals the sum of the digits of the prime factors (3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42). This discovery marked the birth of Smith numbers, named for Wilansky's brother-in-law.

For the full article:

http://sciencenews.org/article.....thtrek.asp

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Questions to explore further this topic:

What is special about these numbers?

http://www.stetson.edu/~efriedma/numbers.html
http://www.math.wichita.edu/hi.....mbers.html

What are "named numbers"?

http://www.tanyakhovanova.com/Numbers/index.html

What are "perfect" numbers?

http://www.sciencenews.org/art.....thtrek.asp

What are "Fibonacci" numbers?

http://www.mcs.surrey.ac.uk/Pe.....ibnat.html

What are "Ruth-Aaron" pairs?

http://www.sciencenews.org/art.....thtrek.asp

What are "Smith" numbers?

http://www.shyamsundergupta.com/smith.htm

What are "Rhonda" numbers?

http://www.wschnei.de/digit-re.....mbers.html

What are "Fermat" numbers?

http://mathworld.wolfram.com/FermatNumber.html

What are special numbers?

Digit-related numbers

http://mathworld.wolfram.com/t.....mbers.html

Divisor-related numbers

http://mathworld.wolfram.com/t.....mbers.html

Fibonacci numbers

http://mathworld.wolfram.com/t.....mbers.html

Figurate numbers

http://mathworld.wolfram.com/t.....mbers.html

Miscellaneous special numbers

http://mathworld.wolfram.com/t.....mbers.html

Number triangles

http://mathworld.wolfram.com/t.....ngles.html