OFFSET
2,2
COMMENTS
The positive solution x to Pi^(x/2)/Gamma(x/2+1) = 1.
Then Pi^(x/2) = 1488.75641500529701...
From Mohammed Yaseen, Sep 25 2022: (Start)
0 is another solution. All other solutions are negative.
This is also the dimension d in which the sphere of unit radius has surface area d. (End)
LINKS
Mohammed Yaseen, Table of n, a(n) for n = 2..10000
Wikipedia, N-sphere
EXAMPLE
12.764052935032681271263280950768574761998...
MATHEMATICA
x /. FindRoot[ Pi^(x/2)/Gamma[x/2 + 1] == 1, {x, 12}, WorkingPrecision -> 105] // RealDigits[#, 10, 105] & // First (* Jean-François Alcover, Feb 12 2013 *)
PROG
(PARI) solve(x=9, 13, Pi^(x/2)-gamma(x/2+1)) \\ Charles R Greathouse IV, Jan 30 2016
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, May 25 2010
STATUS
approved