I chose a certain sequencing rule, and I told my friend no matter what number he named, it would eventually end up at repeating 4s.

At first he chose 5, which ended in 4, 4, 4... Then he tried 18, which met the same fate. Even numbers like -42 and Pi ended in 4, 4, 4...

Still trying to outdo me, he started to get really creative. He tried 63424563562324 ... same. He even tried a googolplex and Avogadro's number. But alas all the numbers he tried ended up in 4,4,4. Finally he conceded.

What's the sequencing rule I use? Should he have conceded? Can you find any starting terms which don't end in 4, 4, 4...?

Might the seuqence be n + 1 = the number of letters which comprise the written form of n?

5
4 (five = 4 letters)
4 (four = 4 letters)
4, etc.

18
8 (eighteen = 8 letters)
5 (eight = 5 letters)
4 (five = four letters)
4, etc.

-42
16 (negative forty-two = 16 letters)
7 (sixteen = 7 letters)
5 (seven = 5 letters)
4, etc.

π
2 (pi = 2 letters)
3 (two = 3 letters)
5 (three = 5 letters)
4, etc.

63424563562324
123 (sixty-three trillion, four hundred twenty-four billion, five hundred sixty-three million, five hundred sixty-two thousand, three hundred twenty-four = 123 letters)
21 (one hundred twenty-three = 21 letters)
9 (twenty-one = 9 letters)
4 (nine = 4 letters)
4, etc.


Four is the only number which contains the same number of letters as it denotes, so any sequence by this rule would eventually reduce to repeating fours.

Posted by Jyqm on 2007-07-31 10:52:32