[seqfan] nearly equal floor(n/Pi) A032615 and A062300

Kevin Ryde user42_kevin at yahoo.com.au
Tue Oct 18 02:20:01 CEST 2016

On the topic of the "nearly equal", searching recently for something
else I found

    A032615(n) = floor(             n  /Pi    );
    A062300(n) = floor( 1/sin(1/( (n+1)/Pi )) );

which are nearly the same (up to offset +1) after the first few values,
since sin(x)~=x when x small.

I make the next difference (after n=6) at n=80143857.  Maybe a fan of
the nearly-equal would be interested.

I imagine n/Pi can fall arbitrarily close to an integer, and with the
sin bigger that may push up across the integer boundary to different
floor().  But the extra the sin adds decreases with n ...

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