Sequence Defined In Terms Of EVERY Term In It

[Paul D Hanna]

        Perhaps A066173 is an example?  

        As I calculate it, there is only one sequence that satisfies the
following:
        a(n) = floor(S^n), where S = sum(k>0, 1/a(k) ), a(1)=1.

Thus the terms are determined uniquely by their reciprocal sum.

The reciprocal sum and the sequence is as follows: 
        S = 1.776791425487658...
and
        A066173 =
{1,3,5,9,17,31,55,99,176,313,557,990,1759,3125,5553,...}

Example: 
        1=[S], 3=[S^2], 5=[S^3], 9=[S^4], 17=[S^5], 31=[S^6], 55=[S^7],
...
where 
        S=1/1 + 1/3 + 1/5 + 1/9 + 1/17 + 1/31 + 1/55 + 1/99 + 1/176 +...

-------------------------------------------------------------------------
On Thu, 27 Feb 03 19:05:37 -0700 Leroy Quet <qqquet at mindspring.com>
writes:
> I posted this to sci.math. I am asking about any sequence in general. 
> But 
> for the purpose of seq.fan, I am asking about integer sequences.
[...]
> 
> I am wondering about any good examples of infinite sequences where
> every terms depends on every other term (prior AND following), and
> where there is only one such sequence which exists given the rule 
> that
> generated it.
> 
[...] 
> Leroy Quet
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