

A119661


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


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
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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



