A074456 Consider surface area 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 surface area.

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

Offset

2,1

Comments

If you set v[n_] := Pi^(n/2)/(n/2)! and s[n_] := n*Pi^(n/2)/(n/2)! and then Plot[{6.283v[n - 2], s[n]}, {n, 0, 20}], the two curves are almost identical.

Links

Table of n, a(n) for n=2..100.

Example

33.1611944849620026918630240155829735800472328410872...

Mathematica

area[d_] := d * Pi^(d/2)/Gamma[d/2 + 1]; area[x /. FindRoot[PolyGamma[x/2] == Log[Pi], {x, 7}, WorkingPrecision -> 120]] (* Amiram Eldar, Jun 08 2023 *)

Crossrefs

The dimension is given in A074455.

Cf. A072478, A072479, A074454.

Sequence in context: A144944 A137426 A269949 * A016454 A065227 A208539

Adjacent sequences: A074453 A074454 A074455 * A074457 A074458 A074459

Keyword

cons,nonn

Author

Robert G. Wilson v, Aug 22 2002

Extensions

Checked by Martin Fuller, Jul 12 2007

Status

approved