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

Kevin Ryde user42_kevin at yahoo.com.au
Sun Oct 23 09:46:55 CEST 2016

cet1 at cam.ac.uk (Chris Thompson) writes:
>        14 25510582 80143857     2.653  **

Ah, I wondered if some rational approximation could help, without
knowing how.  I didn't think to search n=80143857 as one number alone.
It turns up those convergents and some abs(sin(n)) bits becoming them.
Also thrown up is more recent

  A265735 Integers in the interval [Pi*k - 1/k, Pi*k + 1/k] for some k>0.

which dividing through by pi becomes when an n/Pi is within +/-(1/Pi)/k
of some integer k.  Its 1/Pi=0.318 is tighter than Pi/6=0.523.

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