A074454 Consider volume of unit sphere as a function of the dimension d; maximize this as a function of d (considered as a continuous variable); sequence gives decimal expansion of the resulting volume.

5, 2, 7, 7, 7, 6, 8, 0, 2, 1, 1, 1, 3, 4, 0, 0, 9, 9, 7, 2, 8, 2, 1, 4, 5, 8, 6, 4, 1, 7, 2, 8, 4, 6, 3, 8, 7, 5, 2, 9, 9, 9, 9, 2, 8, 4, 5, 1, 0, 1, 7, 3, 5, 6, 7, 7, 6, 1, 6, 3, 7, 3, 4, 0, 2, 1, 4, 8, 6, 4, 1, 2, 7, 3, 0, 5, 4, 7, 0, 1, 7, 1, 1, 0, 0, 6, 2, 0, 4, 8, 4, 0, 7, 2, 5, 8, 4, 0, 1

Offset: 1

Author

Robert G. Wilson v, Aug 22 2002

Keywords

• cons
• nonn

Comments

The dimension is given in A074455.

If you set v(n) = Pi^(n/2)/(n/2)! and s(n) = n*Pi^(n/2)/(n/2)! and then plot {6.283*v(n-2), s(n)} for 0<=n<=20, the two curves are almost identical.

Examples

			5.277768021113400997282145864172846387529999284510173567761637340214864\
12730547017110062048407258401284645...
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 67.

Crossrefs

Cf. A072345, A072346.

Programs

Mathematica

d = x /. FindRoot[ PolyGamma[1 + x/2] == Log[Pi], {x, 5}, WorkingPrecision -> 105]; First[ RealDigits[ Pi^(d/2)/(d/2)!]][[1 ;; 99]] (* Jean-François Alcover, Apr 12 2013 *)

Extensions

Checked by Martin Fuller, Jul 12 2007