A020821 Decimal expansion of 1/8.

1, 2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Also, decimal expansion of Integral_{x=0..oo} x^2/cosh(Pi*x) dx. - Bruno Berselli, Mar 20 2013

Also, decimal expansion of Sum_{i>=1} 1/9^i. - Bruno Berselli, Jan 03 2014

For any triangle ABC, sin(A/2) * sin(B/2) * sin(C/2) <= 1/8, equality is obtained only when the triangle is equilateral (see the Kiran S. Kedlaya link). - Bernard Schott, Sep 16 2022

Examples

			0.12500000000000000000...
		

Links

• Kiran S. Kedlaya, A < B, (1999), Problem 6.3, p. 6.
• Srinivasa Ramanujan, Question 629, Journal of the Indian Mathematical Society, Vol. 7 (1918), p. 40.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A002194, A104956 (other trigonometric inequalities).

Programs

Mathematica

PadRight[{1, 2, 5}, 100] (* Paolo Xausa, Aug 27 2024 *)

Formula

Equals Sum_{k>=1} exp(-Pi*k^2) * (Pi*k^2 - 1/4) (Ramanujan, 1918). - Amiram Eldar, Jan 01 2025