Thursday, November 24, 2005

Number Factoids

Another break in the Thanksgiving cooking. Check out tingilinde: take a number .... I'm far from a mathematician (and was even when I dated one), but I find this list of number facts magical and opaque. These are my favorite of the inscrutable, OCD, and sometimes just silly observations:
  • 4 is the smallest number of colors sufficient to color all planar maps.
  • 11 is the largest known multiplicative persistence.
  • 17 is the number of wallpaper groups.
  • 36 is the smallest number (besides 1) which is both square and triangular.
  • 38 is the last Roman numeral when written lexicographically.
  • 92 is the number of different arrangements of 8 non-attacking queens on an 8x8 chessboard.
  • 136 is the sum of the cubes of the digits of the sum of the cubes of its digits.
  • 405 is a pentagonal pyramidal number.
  • 570 is the product of all the prime palindromic Roman numerals.
  • 1005 is the smallest number whose English name contains all five vowels exactly once.
  • 1084 is the smallest number whose English name contains all five vowels in order.
  • 1435 is a vampire number.
  • 1650 has exactly the same digits in 3 different bases.
  • 1666 is the sum of the Roman numerals.

Anyone know what a vampire number is? An amicable number? And can anyone help him fill in the ???'s? (Huh, looking at the list, I'm reminded that I kind of liked geometry.)

5 comments :

steve said...

It gets worse... someone pointed out that 152 is the smallest positive integer without interesting properties


... of course that makes it interesting leaving 167 as the next number without interesting properites... you can bootstrap a sequence

152, 167, 173, 179. 185 ...

the difference between the second and third, third and fourth, fourth and fifth elements in the series is 6 --- so 666 is embedded in the sequence:-)

Anonymous said...

http://mathworld.wolfram.com/VampireNumber.html
http://mathworld.wolfram.com/AmicablePair.html

Generally, this is a pretty good domain for finding out stuff about math.

Lynn said...

Thank you, anonymous math person! I really like that site.

Lynn said...

steve, that sounds like a math challenge. Find interesting properties for these numbers....

steve said...

I confess a serious love of numbers (as evidenced by listening to a Kate Bush piece http://tingilinde.typepad.com/starstuff/2005/11/wrong_around_th.html ).

The list given shows 1729 as the smallest number representable in two ways as a sum of two cubes ... 1^3 + 12^3 = 9^3 + 10^3. Sadly it leaves out the wonderful story of Hardy and Ramanujan.

It seems Hardy was in a taxi in London when Hardy noted its number was 1729. When he visited Ramanujan he commented on being disappointed with the number and hoped it wasn't a bad omen. Ramanujan immediately said it was a very interesting number.

People refer to Hardy-Ramanujan numbers 1729, 4104 ({2,16], [9,15]) ... an infiniate series.

Sometimes these are called Ramanujan doubles, there are triples and quadruples...