A303658 Decimal expansion of the alternating sum of the reciprocals of the triangular numbers.

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Formula

Equals log(16/e^2) = log(16) - 2.

Equals Sum_{k>=0} 1/((k+2)*2^k) = Sum_{k>=2} 1/A057711(k). - Amiram Eldar, Aug 19 2020

Example

1/1 - 1/3 + 1/6 - 1/10 + 1/15 - 1/21 + ... = 0.77258872223978123766892848583270627230200053744102...

Mathematica

RealDigits[4*Log[2] - 2, 10, 100][[1]] (* Amiram Eldar, Aug 19 2020 *)
RealDigits[Log[16]-2, 10, 120][[1]] (* Harvey P. Dale, Apr 30 2022 *)

Prog

(PARI) sumalt(n=1, (-1)^(n+1)*2/(n*(n+1))) \\ Michel Marcus, Apr 28 2018
(PARI) log(16)-2 \\ Altug Alkan, May 07 2018

Crossrefs

Cf. A000217 (triangular numbers), A057711.

Apart from leading digit the same as A016639 (log(16)).

Sequence in context: A372774 A255272 A335929 * A169812 A195907 A380003

Adjacent sequences: A303655 A303656 A303657 * A303659 A303660 A303661

Keyword

nonn,cons

Author

Jon E. Schoenfield, Apr 28 2018

Status

approved