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

1,3

Links

Table of n, a(n) for n=1..87.

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.

Example

1.07278061334916223879...

Mathematica

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

Prog

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

Crossrefs

Cf. A006566 (dodecahedral numbers).

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

Sequence in context: A096052 A003677 A301864 * A217172 A248791 A253383

Adjacent sequences: A295418 A295419 A295420 * A295422 A295423 A295424

Keyword

nonn,cons

Author

Amiram Eldar, Nov 22 2017

Status

approved