Cont frac with harmonic #s as its terms

Leroy Quet qq-quet at mindspring.com
Thu Oct 13 20:53:20 CEST 2005


I just submitted:

>%S A113064 1,5,67,2035
>%N A113064 a(n) = Numerator of r(n), where r(n) = the continued fraction 
>of rational terms
>[1,3/2,11/6,...,H(n)], where H(n) = sum{j=1..n} 1/j, the nth harmonic number.
>%e A113064 For n = 3 we have 1 + 1/(3/2 + 6/11) = 67/45, the numerator of 
>which is 67.
>%Y A113064 A113065,A001008,A002805
>%O A113064 1
>%K A113064 ,frac,more,nonn,

>%S A113065 1,3,45,1341
>%N A113065 a(n) = Denominator of r(n), where r(n) = the continued fraction 
>of rational terms
>[1,3/2,11/6,...,H(n)], where H(n) = sum{j=1..n} 1/j, the nth harmonic number.
>%e A113065 For n = 3 we have 1 + 1/(3/2 + 6/11) = 67/45, the denominator 
>of which is 45.
>%Y A113065 A113064,A001008,A002805
>%O A113065 1
>%K A113065 ,frac,more,nonn,

Could someone please calculate/submit more terms and also submit the 
simple continued fraction terms (all of which are positive integers) of 
the limit r(n),n-> inf?

thanks,
Leroy Quet






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