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.

1, 2, 4, 6, 22, 30, 45, 53, 211, 242, 429, 554, 917, 1239, 1738, 2161, 2986, 3005, 3101, 3307, 4800, 6385, 7308, 15148, 16668, 19287, 28103, 72754, 143406, 457425, 955117, 1129313, 2290339, 7362039, 11374333, 11711400, 11778444, 11896240, 14221855, 31972242

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Herbert Kociemba, The Spiral of Theodorus

Mathematica

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

Crossrefs

Cf. A072895, A224269.

Sequence in context: A251724 A326363 A273522 * A152482 A045960 A028988

Adjacent sequences: A227623 A227624 A227625 * A227627 A227628 A227629

Keyword

nonn

Author

Herbert Kociemba, Jul 18 2013

Status

approved