cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A080072 Values of n such that Pi^n is farther from its closest integer than any Pi^k for 1 <= k < n.

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%I A080072 #11 Nov 02 2022 12:43:27
%S A080072 1,4,8,31,61,89,200,217,257,1366,3642,4926,20265
%N A080072 Values of n such that Pi^n is farther from its closest integer than any Pi^k for 1 <= k < n.
%C A080072 "Farthest from an integer" only really makes sense if we choose "nearest" or "farthest" integer. I chose nearest here. "Farthest from farthest" would just make "nearest to nearest" and would be sequence A080052. I think.
%e A080072 E.g., Pi^1=3.14159265... Pi^2=9.869..., Pi^3=31.00627..., Pi^4=97.40909... so Pi^4 is farther from 97 (its closest integer) than Pi^3 is from 31, or Pi^2 is from 10.
%p A080072 b := array(1..5000): Digits := 10000: c := 0: pos := 0: for n from 1 to 10000 do: exval := evalf(Pi^n): if (abs(exval-round(exval))>c) then c := (abs(exval-round(exval))): pos := pos+1: b[pos] := n: print(n):fi: od: seq(b[n],n=1..pos);
%o A080072 (PARI) default(realprecision,20000);d=0.0;p=Pi;a=1;for(n=1,40000,a*=p; s=abs(a-round(a));if(s>d,d=s;print1(n,","))) \\ _Robert Gerbicz_, Aug 22 2006
%Y A080072 Cf. A080052, A080053, A079490, A002160.
%K A080072 nonn,more
%O A080072 1,2
%A A080072 Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 24 2003
%E A080072 More terms from _Robert Gerbicz_, Aug 22 2006