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 A172164 #23 May 19 2021 14:57:29 %S A172164 20,19,20,19,20,21,18,21,19,20,20,20,19,20,20,19,20,20,20,19,21,18,21, %T A172164 19,21,18,21,19,21,18,21,19,20,20,20,19,20,20,19,20,20,20,19,20,20,20, %U A172164 19,21,18,21,19,20,20,20,19,20,20,20,19,20,20,19,20,20,20,19,21,18,21 %N A172164 Differences between numbers of triangles entirely contained in two consecutive turns of Pythagoras's snail (Theodorus spiral). %C A172164 Conjecture : The terms are only 18,19,20,21 (From the first thousand turns, there are 2,3% of 18, 36,5% of 19, 46,2% of 20 and 15% of 21). No period found. Probably due to Pi transcendence. %C A172164 From the first one hundred thousand turns, there are 1.662% 18s, 36.350% 19s, 48.393% 20s and 13.595% 21s. - _Robert G. Wilson v_, Mar 31 2013 %C A172164 From the first 10 Million turns, there are 1.69208% 18s, 36.33984% 19s, 48.32320% 20s and 13.64488% 21s. - _Herbert Kociemba_, Jul 15 2013 %F A172164 The second forward difference of A072895. - _Robert G. Wilson v_, Mar 31 2013 %e A172164 In the first turn, 16 triangles are complete. In the 2nd turn, there are 36 triangles completely included. The difference is 20. %t A172164 (* Obtain the sequence of A072895 and set it equal to lst. *); Differences[lst, 2] (* _Robert G. Wilson v_, Mar 31 2013 *) %o A172164 (Python) # See A137515 for Python code, and then OooCalc for more. %Y A172164 Cf. A072895, A137515. %K A172164 nonn %O A172164 2,1 %A A172164 _Sébastien Dumortier_, Jan 27 2010