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A295421 Decimal expansion of the sum of the reciprocals of the dodecahedral numbers (A006566). 4
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified April 17 23:03 EDT 2021. Contains 343071 sequences. (Running on oeis4.)