cp's OEIS Frontend

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

%I A084623 #23 Feb 16 2025 08:32:49
%S A084623 1,1,4,2,16,16,64,16,256,256,1024,512,4096,4096,16384,2048,65536,
%T A084623 65536,262144,131072,1048576,1048576,4194304,1048576,16777216,
%U A084623 16777216,67108864,33554432,268435456,268435456,1073741824,67108864
%N A084623 Numerator of 2^(n-1)/n.
%C A084623 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
%H A084623 Amiram Eldar, <a href="/A084623/b084623.txt">Table of n, a(n) for n = 1..3322</a>
%H A084623 Carlos D'Andrea and Emiliano Gómez, <a href="https://www.jstor.org/stable/27641981">The Broken Spaghetti Noodle</a>, The American Mathematical Monthly, Vol. 113, No. 6 (2006), pp. 555-557.
%H A084623 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TrigonometryAngles.html">Trigonometry Angles</a>.
%H A084623 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SphereLinePicking.html">Sphere Line Picking</a>.
%F A084623 a(n) = 2^(n - A007814(n) - 1).
%F A084623 a(n) = A075101(n)/2.
%e A084623 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
%p A084623 # Assuming offset 0:
%p A084623 seq(2^(n - padic[ordp](n + 1, 2)), n = 0..31); # _Peter Luschny_, May 31 2023
%t A084623 Table[Numerator[2^(n - 1)/n], {n, 40}] (* _Vincenzo Librandi_, Jul 30 2015 *)
%o A084623 (Magma) [Numerator(2^(n-1)/n): n in [1..40]]; // _Vincenzo Librandi_, Jul 30 2015
%o A084623 (PARI) vector(50, n, numerator(2^(n-1)/n)) \\ _Michel Marcus_, Jul 30 2015
%Y A084623 Cf. A000265 (denominators), A007814, A075101.
%K A084623 nonn,frac
%O A084623 1,3
%A A084623 _Eric W. Weisstein_, Jun 01 2003