[seqfan] CF for Constant A071873
Paul D Hanna
pauldhanna at juno.com
Sun May 10 04:41:57 CEST 2015
Seqfans,
Consider the continued fraction of the constant described by http://oeis.org/A071873 ;
The constant x satisfies: x = Sum_{n>=0} ( floor(10*n*x) (mod 10) ) / 10^n
and begins:x = 0.50505050505050505051616161616161616161627272727272727272727383838383838383838384949494...
I get the following partial quotients:
contfrac(x) = [0, 1, 1, 48, 1, 9182736455463727, 4, 1, 2, 1, 3, 1,
16413861141941053151166388889231063606316227031696978138434,
9, 9, 2, 1, 3, 8, 1, 1, 19, 1, 1, 2, 3, 1, 7, 1, 1, 4, 1, 1, 1,
3, 3, 1, 1, 2, 2, 2, 1, 5, 2, 1, 1, 1, 1, 5, 1, 78, 1, 21, 1, 1, 5, 3, 2]
but 50,000 digits of x will not yield more partial quotients!
Could someone try to compute the next few partial quotients?
I suspect the next partial quotients to involve a very large integer.
>From the definition of x, one does not expect x to have a finite continued fraction!
Thanks,
Paul
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