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11

Part of PEN N Problems

Problems(1)

N 11

Source:

5/25/2007
The infinite sequence of 2's and 3's 2,3,3,2,3,3,3,2,3,3,3,2,3,3,2,3,3,3,2,3,3,3,2,3,3,3,2,3,3,2,3,3,3,2,⋯\begin{array}{l}2,3,3,2,3,3,3,2,3,3,3,2,3,3,2,3,3, \\ 3,2,3,3,3,2,3,3,3,2,3,3,2,3,3,3,2,\cdots \end{array} has the property that, if one forms a second sequence that records the number of 3's between successive 2's, the result is identical to the given sequence. Show that there exists a real number rr such that, for any nn, the nnth term of the sequence is 2 if and only if n=1+⌊rm⌋n = 1+\lfloor rm \rfloor for some nonnegative integer mm.
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