A295421 Decimal expansion of the sum of the reciprocals of the dodecahedral numbers (A006566).

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

Offset: 1

Author

Amiram Eldar, Nov 22 2017

Keywords

• nonn
• cons

Examples

			1.07278061334916223879...
		

Crossrefs

Cf. A006566 (dodecahedral numbers).

Sums of inverses: A152623 (tetrahedral numbers), A002117 (cubes), A175577 (octahedral numbers), A175578 (icosahedral numbers).

Programs

Mathematica

RealDigits[Sum[2/(n(3n-1)(3n-2)), {n, 1, Infinity}], 10, 100][[1]]

PARI

(sqrt(3)*Pi - 3*log(3))/2 \\ Michel Marcus, Nov 23 2017

Formula

Sum_{n>=1} 2/(n(3n-1)(3n-2)) = 1/1 + 1/20 + 1/84 + 1/220 + 1/455 + ... = (sqrt(3)*Pi - 3*log(3))/2.