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A book that you be interested in is "Curious and Interesting Numbers" by David Wells.
It has a whole load of numbers, all put in numerical order, so its almost like a number dictionary.
Opening it at random i find things such as:
371 = 3<sup>3</sup> + 7<sup>3</sup> + 1<sup>3</sup>
12,321 = 111<sup>2</sup>, also 1,234,321 = 1111<sup>2</sup>, etc.
3,628,800
Equal to 10! and the only factorial that is the product of other consecutive factorials (apart from the trivial ones involving 1!).
10! = 6! * 7!
10! also equals 3! * 5! * 7!.
These examples are all very short, but some of the explainations go on for paragraphs or even pages (esp. pi, e, phi, etc.).
Interesting book, but not exactly cover to cover reading!
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