A353127 Decimal expansion of Pi^2/4 - log(2).

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

Offset: 1

Author

Bernard Schott, Apr 24 2022

Keywords

• nonn
• cons

Comments

Limit of the series u where u(n) = 1/n when n is a square, and u(n) = (-1)^n/n otherwise.

Examples

			1.77425391971239434529139062851086121575292471744...
		

References

• M. Lepez, Les Grands classiques de Mathématiques, Classes préparatoires scientifiques, Analyse, Exercices corrigés et commentés, MP-PC-PT, Bréal, 1995, Exercice 201, p. 29.

Crossrefs

Cf. A091476 (Pi^2/4), A002162 (log(2)).

Programs

Maple

evalf(Pi^2/4 - log(2),100);

Mathematica

RealDigits[Pi^2/4 - Log[2], 10, 100][[1]] (* Amiram Eldar, Apr 24 2022 *)

PARI

Pi^2/4 - log(2) \\ Michel Marcus, Apr 24 2022

Formula

Equals A091476 - A002162.

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