A175477 Decimal expansion of the dimension in which the sphere of unit radius has unit volume.

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

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

Cf. A074455, A074457.

Sequence in context: A135155 A308705 A244847 * A333521 A359533 A333205

Adjacent sequences: A175474 A175475 A175476 * A175478 A175479 A175480

Keyword

cons,easy,nonn

Author

R. J. Mathar, May 25 2010

Status

approved