Stern's diatomic series - frequencies

[franktaw at netscape.net]

This is A002487.

I was looking at the frequencies of different numbers in
this sequence.  Every odd prime from 3 through 29 takes
a turn at being the term that occurs most often in an
initial segment of the sequence (although not perfectly
in order).  Then at n = 6122, suddenly 71 becomes the
most common, and stays there through n = 16384
(which is as far as I looked).

What's so special about 71?

What happens for larger values of n?  Is the most common
value ever composite?

Franklin T. Adams-Watters

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