LOGOLOG
a weblog of wordplay by Eric Harshbarger

## Favorite Number

Until today if you had asked me what my favorite number was, I probably would have simply said I did not have one. I think that has changed. I'm not going with 0, or 1, or 3, or 7, or 13. I'm not going to get math-nerdy and go with PI, or e, or i. No, I'm going to get even nerdier. I'm choosing this monster, which I just discovered today, as my favorite number:

3,000,000,000,000,000,013,019,000,000,000

Is it not clear why I've chosen this?

Okay, maybe it's not obvious. Let me explain. If you were to spell this number out, it would be THREE NONILLION THIRTEEN TRILLION NINETEEN BILLION*. The number-name is forty-five letters long. But more interestingly is the frequency of the letters that spell it. Here is a count of the letters:

```B = 1
H = 2
R = 3
O = 4
T = 5
L = 6
E = 7
I = 8
N = 9
```
As far as I know, this is the only number-name of any length whose letter frequencies can be arranged in an ascending sequence like that. Well, there are actually five other number-names similar to the one above (by rearranging the order of the THREE/THIRTEEN/NINETEEN words) -- I've chosen the combination of least value, and just consider the others equivalent instances.

If anyone is able to find another number, of any name-length, that exhibits this quality, please let me know.

-- Eric

* I should point out my (pretty standard) assumptions for number-names. First, I'm using the "short-scale" notation (where a billion is 1,000,000,000; and so on). Secondly, the word "and" is not used when spelling out the number-name (as is sometimes done in cases like "five hundred AND thirty-two"). Finally, the hundreds unit is never modified by more than a single-digit number (for example, "seventeen hundred" would not be considered valid; it should be "one thousand seven hundred").

[7 August 2012]

Archive

Update: Mike Keith has pointed out to me that the "billion" can be replaced with "million." Not only does this create a number of lesser value, it shows that there is more than one answer to the challenge.

Posted by: Eric Harshbarger

Well, I've found another example of this type of number. It's fifty-eight digits long:

9,000,000,000,000,000,000,000,010,000,000,000,000,000,000,019,000,000,000,000

NINE OCTODECILLION TEN DECILLION NINETEEN TRILLION

Posted by: Eric Harshbarger

I found this numbers in Spanish :

Seiscientos once nonillones setecientos dieciseis

: 1 d, 2 l, 3 t, 4 c, 5 o, 6 n, 7 i, 8 s y 9 e.

and

Un octodecillón doscientos cinco nonillones seiscientos cinco:

1 u, 2 d, 3 t, 4 l, 5 e, 6 s, 7 i, 8 c, 9 n y 10 o.

Posted by: Claudio Meller

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