[seqfan] Re: what is most special about a given integer?

[Olivier Gerard]

Hello Eric,

Nice page.

A better categorization of 168 to my taste is: 
the smallest non cyclic simple group which is not an alternative group.

a few numbers not in your list which have interesting decompositions
into perfect powers

117 = 9 + 27 + 81 = 3^2 + 3^3 + 3^4
287 = 4 + 27 + 256 = 2^2 + 3^3 + 4^4
698 = 9 + 64 + 625 = 3^2 + 4^3 + 5^4
1130 = 169 + 961 = 13^2 + 31^2
1553 = 529 + 1024 = 23^2 + 32^2
1877 = 196 + 1681 = 14^2 + 41^2

(extract of sequences I am going to submit to the eis)

For a lot of numbers in the 1900->2000 range, I think you can look
at Olympiads and Problem contests as it is a classical topics for 
authors to build a problem around the year of the contest.

It would be good to give a rate to your categorizations, so that people can spot
things you have chosen for want of better.

As a true seqfan, you should add links to the EIS sequences refered in the definitions
so that people could learn a lot if they want.

As a scholar you should cite your sources and your methods
somewhere on the page or on the site.

Olivier


On Wed, May 30, 2001 at 11:16:29AM -0400, Erich Friedman wrote:
> greetings seq fans.
> 
> for a couple years now i've been working on a list of the most distinctive
> fact about each small positive integer.  for example, 12 is the smallest
> abundant number, 52 is a bell number, 76 is automorphic, and 153 is the sum
> of the cubes of its digits.  for space reasons i've only been concentrating
> on numbers below 10,000.
> 
> i've considered entries from "the lure of integers", "the penquin
> dictionary of curious and interesting numbers", and "the kingdom of
> infinite number", as well as looked at all the "core" sequences at the EIS.
> are there other sources that i have missed?
> 
> the current list can be found at:
> http://www.stetson.edu/~efriedma/numbers.html  please let me know about any
> additions, suggestions, or corrections.  thanks.
> 
> erich friedman
> 
> 
>