Caterpillar NumbersType B
Pick a natural number n<100
Rewrite the number n = 10T + U, where U is the unit's digit and T is the ten's digit
The next number segment in the caterpillar number is 4U+T
Repeat using your new result as n
The caterpillar number ends when its "head" equals its "tail"
The chain of numbers becomes a caterpillar number of Type B.
For example, two caterpillar numbers of this type are 1293627303129 and 624183315216.
Some Questions To Explore:
 Are all such caterpillar numbers finite in length?
 What is the shortest caterpillar number you can find? Longest?
 Is there a pattern formed by caterpillar numbers of the same length?
 Is there an "evenoddeven...odd..." caterpillar number?
 What is special about the number 13?
 What happens if you try initial nvalues greater than 100?
 What are caterpillar numbers of Type A....see the previous problem in the Archive?
Extension: Expand your exploration by trying 2U+T, 3U+T, 5U+T, etc....
Some Trivia: The diagram is part of a fabric called "Caterpillar Numbers," available online.
Source: J.M. (Bellingham)...who loves to explore number patterns.
Hint: Again, you just need to play with this pattern. No real "answer" is the goal....rather the goal is the discovery process itself.
Solution Commentary: Send me your discoveries....I am prepared to include them as part of this commentary.
I am especially interested in proofs or arguments relative to the special nature of 13 and the generalization to n>100 or for the rule pU+t for p a natutal number.
