cp's OEIS Frontend

The "curling number" k = k(S) of a string of numbers S = s(1), ..., s(m) is defined as follows. Write S as XY^k for strings X and Y (where Y has positive length) and k is maximized, i.e., k = the maximal number of repeating blocks at the end of S.

The "tail length" t(S) of S is defined as follows: start with S and repeatedly append the curling number (recomputing it at each step) until a 1 is reached; t(S) is the number of terms that are appended to S before a 1 is reached.

If a 1 is never reached, set t(S)=oo (the Curling Number Conjecture says this will never happen).

A sequence S in {2,3}* is called "rotten" if either of t(2S) or t(3S) (or both) is strictly less than t(S).

Example: S = 32323 has curling number k=2, so we get 323232; now k=3, so we get 3232323; now k=3, so we get 32323233; now k=2, so we get 323232332; now k=1 so we stop. We added 4 terms before reaching 1, so t(S)=4.

On the other hand, 2S = 232323 only extends to 232323321..., so t(2S)=2 which means S is rotten.