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A175477
Decimal expansion of the dimension in which the sphere of unit radius has unit volume.
1
1, 2, 7, 6, 4, 0, 5, 2, 9, 3, 5, 0, 3, 2, 6, 8, 1, 2, 7, 1, 2, 6, 3, 2, 8, 0, 9, 5, 0, 7, 6, 8, 5, 7, 4, 7, 6, 1, 9, 9, 8, 4, 0, 4, 7, 3, 2, 5, 6, 1, 4, 3, 7, 0, 6, 0, 5, 8, 7, 5, 7, 2, 0, 7, 4, 1, 3, 0, 0, 9, 6, 0, 2, 7, 2, 5, 6, 1, 9, 6, 2, 2, 0, 8, 2, 7, 1, 0, 6, 4, 7, 8, 3, 6, 4, 9, 0, 5, 4, 6, 6, 9, 5, 4, 8
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
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
Sequence in context: A135155 A308705 A244847 * A333521 A359533 A333205
KEYWORD
cons,easy,nonn
AUTHOR
R. J. Mathar, May 25 2010
STATUS
approved