A084623 Numerator of 2^(n-1)/n.

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

Offset: 1

Author

Eric W. Weisstein, Jun 01 2003

Keywords

• nonn
• frac

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

Examples

			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
		

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.

Crossrefs

Cf. A000265 (denominators), A007814, A075101.

Programs

Magma

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

Maple

# Assuming offset 0:
seq(2^(n - padic[ordp](n + 1, 2)), n = 0..31); # Peter Luschny, May 31 2023

Mathematica

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

PARI

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

Formula

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

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