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

Author

R. J. Mathar, May 25 2010

Keywords

• cons
• easy
• nonn

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)

Examples

			12.764052935032681271263280950768574761998...
		

Links

• Mohammed Yaseen, Table of n, a(n) for n = 2..10000
• Wikipedia, N-sphere

Crossrefs

Cf. A074455, A074457.

Programs

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 *)

PARI

solve(x=9,13,Pi^(x/2)-gamma(x/2+1)) \\ Charles R Greathouse IV, Jan 30 2016