[seqfan] Re: CF for Constant A071873

[C Boyd]

> 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!

The convergent implied by the CF (up to the last known term) has an interesting denominator: in Pari,

contfrac(56116722783389450057351290684624017957363636363636363636363759820426487093153761054994388327721660/((10^99-1)/9))
%1 = [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]

The numerator is less interesting (apart from the run of 36's):

factor(56116722783389450057351290684624017957363636363636363636363759820426487093153761054994388327721660)
%2 = 
[2 2]

[5 1]

[2805836139169472502867564534231200897868181818181818181818187991021324354657688052749719416386083 1]

The corresponding convergents implied by the CF up to the terms before the known massive terms, 50/99 and 41322314049586776860/81818181818181818181, also have suggestive denominators.

Best wishes,

CB