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Telephone Numbers - February 21, 2013
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Spiked Math Comic - Telephone Numbers

Relevant link: http://en.wikipedia.org/wiki/Telephone_number_(mathematics)

Also called the involution numbers, they can be determined by the recurrence:

      a_0 = a_1 = 1;
      a_n = a_{n−1} + (n − 1) a_{n−2}, for n > 1.

More interesting, they also count the number of involutions on a set with n elements -- note that an involutary function, is a function f that is its own inverse, that is,

     f(f(x)) = x for all x in the domain of f.

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If I would enter one of the numbers in my phone, I would call (the family of) a former classmate of mine. :)
But that just works because in germany short numbers are automatically prepended with the local area code. :S

(480) 970-1440. Only ten-digit one.

Yeah, but there's also 2390480 (the 7-disit one). Most phones just stick the area code in automatically. Not to mention outside the U.S., there are phone numbers of other lengths.

This is integer sequence A000085 (see http://oeis.org/A000085).

In this sequence, a(n) is the number of partitions of a set of n distinguishable elements into subsets of size 1 and 2 (from Karol A. Penson).

Wow, I can't believe Spiked Math is famous enough now to get spam like the comment above.

*Comment was removed*
I used to get 20-30 spam comments a day but because of my fancy derivative question it's down to about 0-2 per day (except one day when there was like 100 spam comments, 1 every 2-3 minutes).

Wait... that derivative question actually worked?

I wonder how many calls Cheryl Porcelli of Scottsdale, Arizona, has gotten over this.

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