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A084623 Numerator of 2^(n-1)/n. 16
1, 1, 4, 2, 16, 16, 64, 16, 256, 256, 1024, 512, 4096, 4096, 16384, 2048, 65536, 65536, 262144, 131072, 1048576, 1048576, 4194304, 1048576, 16777216, 16777216, 67108864, 33554432, 268435456, 268435456, 1073741824, 67108864 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

n/2^(n-1) is the probability that when a stick is broken up at n-1 points independently and uniformly chosen at random along its length the n pieces cannot form an n-gon (D'Andrea and Gómez, 2006). - Amiram Eldar, Dec 04 2020

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..3322

Carlos D'Andrea and Emiliano Gómez, The Broken Spaghetti Noodle, The American Mathematical Monthly, Vol. 113, No. 6 (2006), pp. 555-557.

Eric Weisstein's World of Mathematics, Trigonometry Angles.

Eric Weisstein's World of Mathematics, Sphere Line Picking.

FORMULA

a(n) = 2^(n - A007814(n) - 1).

a(n) = A075101(n)/2.

EXAMPLE

The first few fractions are 1, 1, 4/3, 2, 16/5, 16/3, 64/7, 16, 256/9, 256/5, 1024/11, 512/3, 4096/13, 4096/7, 16384/15, 2048, 65536/17, 65536/9, 262144/19, 131072/5, 1048576/21, 1048576/11, 4194304/23, 1048576/3, ... - N. J. A. Sloane, Mar 18 2018

MATHEMATICA

Table[Numerator[2^(n - 1)/n], {n, 40}] (* Vincenzo Librandi, Jul 30 2015 *)

PROG

(MAGMA) [Numerator(2^(n-1)/n): n in [1..40]]; // Vincenzo Librandi, Jul 30 2015

(PARI) vector(50, n, numerator(2^(n-1)/n)) \\ Michel Marcus, Jul 30 2015

CROSSREFS

Cf. A000265 (denominators), A007814, A075101.

Sequence in context: A053125 A038232 A254632 * A264195 A182872 A137393

Adjacent sequences:  A084620 A084621 A084622 * A084624 A084625 A084626

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Jun 01 2003

STATUS

approved

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Last modified May 16 14:39 EDT 2021. Contains 343949 sequences. (Running on oeis4.)