Stern's diatomic series - frequencies

[Edwin Clark]

On Wed, 13 Sep 2006 franktaw at netscape.net wrote:

> 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?
> 

Well, I computed the most frequent values in a(0), a(1),a(2),...,a(10^6)

and found that among the top 73 most frequent values all were prime.
I think something strange is going on here.

Here's the distribution for these terms. The most frequent is 419 which
occurs 795 times.

[[419, 795], [701, 767], [619, 761], [433, 759], [661, 753], [431, 753], 
[479, 749], [839, 746], [647, 743], [653, 741], [379, 739], [461, 739], 
[337, 738], [587, 737], [499, 736], [557, 735], [541, 734], [373, 734], 
[523, 732], [463, 729], [547, 728], [421, 728], [577, 728], [389, 728], 
[397, 727], [823, 726], [613, 725], [563, 724], [503, 723], [733, 723], 
[359, 722], [449, 717], [607, 717], [467, 716], [241, 716], [599, 715], 
[941, 715], [443, 715], [509, 711], [367, 711], [271, 711], [439, 709], 
[487, 706], [643, 706], [677, 705], [787, 705], [821, 705], [673, 704], 
[631, 704], [383, 703], [313, 703], [349, 702], [811, 701], [353, 700], 
[307, 700], [457, 698], [521, 696], [659, 696], [773, 696], [401, 696], 
[409, 696], [683, 695], [331, 695], [641, 695], [239, 695], [907, 695], 
[797, 694], [347, 693], [691, 693], [571, 693], [263, 692], [251, 689], 
[569, 688]]