A365524 Decimal expansion of 4*log(2) - 5/2.

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

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) = (3*k^2 - k)/(k^2 + k) is the ratio between the k-th pentagonal and triangular numbers.

Examples

			0.27258872223978123766892848583270627230200053744102...
		

Links

• Michael Ian Shamos, A catalog of the real numbers (2011), p. 330.
• Wikipedia, Polygonal number.
• Index entries for transcendental numbers

Crossrefs

Cf. A002162.

Cf. A000217, A000326, A358517.

Essentially the same as A016639 and A358517.

Programs

Mathematica

RealDigits[4*Log[2] - 5/2, 10 , 100][[1]] (* Amiram Eldar, Sep 08 2023 *)

PARI

4*log(2)-5/2

Formula

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

Equals Sum_{k>=1} (-1)^(k+1)*(3*k^2 - k)/(k^2 + k).