[seqfan] Pi Day Question
q1qq2qqq3qqqq at yahoo.com
Sat Mar 14 21:07:30 CET 2009
[Whoops. I accidently sent this to seqfan at seqfan.com. Resending to correct address now...]
Happy Pi Day, everybody! (At least in the US, where it is still March 14 and where the date is written 3/14.)
A pi question:
Consider the simple continued faction of pi. (The terms of which are sequence A001203.)
The comment at the related sequence A032523 (A032523(n) = the index of the first occurrence of n in A001203) suggests that it is not known for certain that every positive integer occurs in the simple continued fraction of pi.
Can it be said, however, that either: it is known that each positive integer that does occur occurs infinitely often; OR it is known that at least some integers occur finitely often?
I am not even sure, from what little I have read, that if is known that 1 occurs infinitely often in the continued fraction of pi.
Can anyone enlighten me (and us)?
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