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 fortytwo = 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 (sixtythree trillion, four hundred twentyfour billion, five hundred sixtythree million, five hundred sixtytwo thousand, three hundred twentyfour
= 123 letters)
21 (one hundred twentythree = 21 letters)
9 (twentyone = 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 20070731 10:52:32 