[seqfan] Re: Little puzzle

[Allan Wechsler]

Slightly confused; when you say f(), do you mean S()? Or did you omit a
definition?

If f=S, then your first sum is a sum over a sequence of sequences, and it's
unclear to me just what you want to get back.


On Tue, Apr 10, 2018 at 5:57 PM, David Wilson <davidwwilson at comcast.net>
wrote:

> Let r(k) = [k + 1/2] = k rounded to the nearest integer.
>
> For integer n >= 0, define the sequence
>
> S(k) = { r(k/2^n) : n  >= 1 }
>
> So, for example, we have
>
> f(11) = (r(11/2), r(11/4), r(11/8), ...) = (6, 3, 1, 1, 0, 0, 0, ...)
>
> What are
>
> SUM(k = 1..inf, f(k))
> SUM(k = 1..inf, 2^k f(k)^2)
>
>
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