Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #23 May 19 2021 14:57:29
%S 20,19,20,19,20,21,18,21,19,20,20,20,19,20,20,19,20,20,20,19,21,18,21,
%T 19,21,18,21,19,21,18,21,19,20,20,20,19,20,20,19,20,20,20,19,20,20,20,
%U 19,21,18,21,19,20,20,20,19,20,20,20,19,20,20,19,20,20,20,19,21,18,21
%N Differences between numbers of triangles entirely contained in two consecutive turns of Pythagoras's snail (Theodorus spiral).
%C 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 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 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 The second forward difference of A072895. - _Robert G. Wilson v_, Mar 31 2013
%e In the first turn, 16 triangles are complete. In the 2nd turn, there are 36 triangles completely included. The difference is 20.
%t (* Obtain the sequence of A072895 and set it equal to lst. *); Differences[lst, 2] (* _Robert G. Wilson v_, Mar 31 2013 *)
%o (Python) # See A137515 for Python code, and then OooCalc for more.
%Y Cf. A072895, A137515.
%K nonn
%O 2,1
%A _Sébastien Dumortier_, Jan 27 2010