A164109 Decimal expansion of Pi^4/3.

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

Offset: 2

Author

R. J. Mathar, Aug 10 2009

Keywords

• cons
• nonn

Comments

Surface area of the 8-dimensional unit sphere.

Examples

			32.4696970113341457454801108962350370832425285...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 2..5000
• Eric Weisstein's World of Mathematics, Hypersphere.
• Wikipedia, Hypersphere.
• Ce Xu and Jianqiang Zhao, Sun's Three Conjectures on Apéry-like Sums Involving Harmonic Numbers, arXiv:2203.04184 [math.NT], 2022.
• Index entries for transcendental numbers.

Crossrefs

Cf. A019692, A019694, A164102, A164104, A091925, A164107.

Cf. A001008, A002805.

Programs

Mathematica

RealDigits[Pi^4/3,10,120][[1]] (* Harvey P. Dale, Jul 31 2014 *)

PARI

Pi^4/3 \\ G. C. Greubel, Sep 11 2017

Formula

Equals 8*A164108 = A019670*A091925 = A092425/3.

Pi^4/30 = Sum_{k>=1} H(k)*H(k+1)/(k+1)^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, Aug 19 2025