A119661 a(n) = floor(Pi/arccos(n/(n+1))).

3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19

Offset

1,1

Comments

Let N(m1, m2, m3) be the maximum possible number of pairwise elastic collisions in a dynamic system of 3 point masses m1, m2, m3 on a line. N(m1,m2, m3) is independent of initial velocities and coordinates of masses m1, m2, m3. If m1 = n*m2 = m3 then N(m1, m2, m3) = -[-Pi/arccos(sqrt(m1*m3/((m1+m2)*(m2+m3))))] = a(n).

Links

Muniru A Asiru, Table of n, a(n) for n = 1..1000

G. A. Galperin, A. N. Zemliakov, Mathematical Billiards, "KVANT" Library, Issue 77, Moscow, Nauka, 1990, p. 165. (in Russian)

Example

n = 24, -Pi/arccos(n/(n+1)) = -11.06997134, [-11.06997134] = -11. Therefore a(24) = 11.

Maple

seq(-trunc(-Pi/arccos(n/(n+1))), n=1..76); # Peter Luschny, Jun 28 2018

Mathematica

Table[ -IntegerPart[ -Pi/ArcCos[ n/(n+1) ] ], {n, 1, 100}]

Crossrefs

Sequence in context: A075324 A134993 A011375 * A285269 A285786 A120196

Adjacent sequences: A119658 A119659 A119660 * A119662 A119663 A119664

Keyword

nonn

Author

Alexander Adamchuk, Jul 28 2006

Extensions

Edited by Peter Luschny, Jun 29 2018

Status

approved