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.
%I A115790 #15 Apr 13 2024 12:42:20 %S A115790 0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0, %T A115790 0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0, %U A115790 0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0 %N A115790 a(n) = 1 - (floor((n+1)*Pi) - floor(n*Pi)) mod 2. %C A115790 The arithmetic mean 1/(n+1)*sum(a(k)|k=0...n) converges to Pi-3. What is effectively the same: the Cesaro limit (C1) of a(n) is Pi-3. %F A115790 a(n) = 1 - (Floor((n+1)*Pi)-Floor(n*Pi)) mod 2. %F A115790 a(n) = 1 - A115789(n). - _Michel Marcus_, Jul 15 2013 %e A115790 a(6)=0 because 7*Pi=21.99, 6*pi=18.85 and so a(6)=1-(21-18) mod 2 = 0; %e A115790 a(7)=1 because 8*Pi=25.13 and so a(7)=1-(25-21) mod 2 = 1; %t A115790 Mod[1-(Last[#]-First[#]),2]&/@(Partition[Floor[Pi #]&/@ Range[ 0,110],2,1]) (* _Harvey P. Dale_, Oct 12 2012 *) %Y A115790 Cf. A000796, A022844, A063438, A115788, A115789. %K A115790 nonn %O A115790 0,1 %A A115790 _Hieronymus Fischer_, Jan 31 2006