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

2,1

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

Links

Table of n, a(n) for n=2..70.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A072895, A137515.

Sequence in context: A022976 A023462 A261307 * A267058 A205545 A087708

Adjacent sequences: A172161 A172162 A172163 * A172165 A172166 A172167

Keyword

nonn

Author

Sébastien Dumortier, Jan 27 2010

Status

approved