A365523 Decimal expansion of 6*log(2) - 4.

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

Offset: 0

Author

Claude H. R. Dequatre, Sep 08 2023

Keywords

• nonn
• cons

Comments

This sequence is also the decimal expansion of Sum_{k>=1} (-1)^(k+1)*f(k), where f(k) = (4*k^2 - 2*k)/(k^2 + k) is the ratio between the k-th hexagonal and triangular numbers.

Examples

			0.15888308335967185650339272874905940845300080616153...
		

Links

• Michael Ian Shamos, A catalog of the real numbers (2011), p. 219.
• Wikipedia, Polygonal number.
• Index entries for transcendental numbers

Crossrefs

Cf. A002162. Essentially the same as A016687.

Cf. A000217, A000384.

Programs

Mathematica

RealDigits[6*Log[2] - 4, 10 , 100][[1]] (* Amiram Eldar, Sep 08 2023 *)

PARI

6*log(2)-4

Formula

Equals Sum_{k>=1} k/(2^k*(k + 1)*(k + 2)) [Shamos].

Equals Sum_{k>=1} (-1)^(k+1)*(4*k^2 - 2*k)/(k^2 + k).