Asymptote of A003242

[hv at crypt.org]

Maple gives
1.7502412917183090312497386246398158787782058181381590561316586131751935167152

No chance of a closed form, I think.

Brendan.

* hv at crypt.org <hv at crypt.org> [080805 13:11]:
> By my calculation, A003242(n) should tend to k^n, where k is given by:
>   1 = sum_i=1^inf{ 1/(k^i + 1) }
> 
> By numerical methods I find k ~= 1.750241291718309, can anyone suggest
> how to solve that equation to get a closed form?
> 
> Actual values seem to support this; here are some selected cases:
> 
>     n: a(n)^(1/n)
> ====================
>     1: 1.0
>     2: 1.0
>     4: 1.41421356237
>     8: 1.58082238074
>    16: 1.66658717253
>    32: 1.70785645051
>    64: 1.7289190436
>   128: 1.73954749867
>   256: 1.7448862029
>   512: 1.7475616961
>  1024: 1.74890098071
>  2048: 1.74957100787
>  4096: 1.7499061177
>  8192: 1.75007369668
> 16384: 1.7501574922
> 
> Hugo