[seqfan] Re: A172265 solutions sin(1/x)=0

[Kevin Ryde]

yae9911 at gmail.com (Hugo Pfoertner) writes:
>
> So the remaining question is: Is there any reasonable rewording
> ... other than "partial sums of A024820"

The only contrived function I thought for a "count solutions" style
could be repeat regions of sin in some way.  Eg. x = k to k+1 maps to
sin of 1 to 2^k by

    f(x) = sin(1 + frac(x)*(2^floor(x)-1))

where frac(x) = x-floor(x) fractional part of x.  Count solutions f(x)=0
in 0 <= x < n is then sin 1 to 2^k over each k<=n.  There'd be a
discontinuity in f(x) at each integer x, which is unattractive.  I don't
know any calculus standard along these lines (as opposed to the
motivating sin(1/x) which is a standard).