A172164 Differences between numbers of triangles entirely contained in two consecutive turns of Pythagoras's snail (Theodorus spiral).

20, 19, 20, 19, 20, 21, 18, 21, 19, 20, 20, 20, 19, 20, 20, 19, 20, 20, 20, 19, 21, 18, 21, 19, 21, 18, 21, 19, 21, 18, 21, 19, 20, 20, 20, 19, 20, 20, 19, 20, 20, 20, 19, 20, 20, 20, 19, 21, 18, 21, 19, 20, 20, 20, 19, 20, 20, 20, 19, 20, 20, 19, 20, 20, 20, 19, 21, 18, 21

Offset: 2

Author

Sébastien Dumortier, Jan 27 2010

Keywords

• nonn

Comments

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.

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

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

Examples

			In the first turn, 16 triangles are complete. In the 2nd turn, there are 36 triangles completely included. The difference is 20.
		

Crossrefs

Cf. A072895, A137515.

Programs

Mathematica

(* Obtain the sequence of A072895 and set it equal to lst. *); Differences[lst, 2] (* Robert G. Wilson v, Mar 31 2013 *)

Python

# See A137515 for Python code, and then OooCalc for more.

Formula

The second forward difference of A072895. - Robert G. Wilson v, Mar 31 2013