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A227626 Consider the spiral of Theodorus (A072895). This sequence is closely related to A224269 and gives the number of k successive revolutions such that the triangles are closer to 360 degrees than any previous triangles.

%I A227626 #11 Sep 28 2013 16:17:18
%S A227626 1,2,4,6,22,30,45,53,211,242,429,554,917,1239,1738,2161,2986,3005,
%T A227626 3101,3307,4800,6385,7308,15148,16668,19287,28103,72754,143406,457425,
%U A227626 955117,1129313,2290339,7362039,11374333,11711400,11778444,11896240,14221855,31972242
%N A227626 Consider the spiral of Theodorus (A072895). This sequence is closely related to A224269 and gives the number of k successive revolutions such that the triangles are closer to 360 degrees than any previous triangles.
%H A227626 Herbert Kociemba, <a href="http://kociemba.org/themen/spirale/theodorus.html">The Spiral of Theodorus</a>
%t A227626 k=minDist=1; lst={}; K=-2.1577829966594462209291427868295777235; num[n_] := Module[{a=-(K/2)+n Pi,b}, b=a^2-1/6; If[Floor[b]==Floor[b+1/(144 a^2)], Floor[b], Undefined]] While[k<40000000, n=num[k]; If[!NumberQ[n], Print[k," Stop"]; Break[]]; a=2Pi-Mod[K+2 Sqrt[n]+1/(6 Sqrt[n]),2Pi]; b=Mod[K+2 Sqrt[n+1]+1/(6 Sqrt[n+1]),2Pi]; If[a<minDist && a<b, AppendTo[lst,k]; minDist=a;]; If[b<minDist && b<a, AppendTo[lst,k]; minDist=b;]; k++]; lst
%Y A227626 Cf. A072895, A224269.
%K A227626 nonn
%O A227626 1,2
%A A227626 _Herbert Kociemba_, Jul 18 2013