A254666 Decimal expansion of the right Alzer's constant.

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

Offset

0,1

Comments

The right Alzer's constant x is defined to be the best constant in the right Alzer's inequality: abs(cos a + sin a) <= x*abs(cos(cos a) + cos(sin a)), where a is any real number.

Links

Table of n, a(n) for n=0..106.

Horst Alzer, A trigonometric double-inequality, Elemente der Mathematik 65 (2010), 45-48.

Formula

Equals (sqrt(2)*cos(1/sqrt(2)))^(-1).

Example

0.9301043163036166822994530624072616003335332058073463854808289441...

Mathematica

RealDigits[1/(Sqrt[2]*Cos[1/Sqrt[2]]), 10, 120][[1]] (* Amiram Eldar, Jun 12 2023 *)

Prog

(PARI) 1/(sqrt(2)*cos(1/sqrt(2))) \\ Michel Marcus, Feb 05 2015

Crossrefs

Cf. A254615.

Sequence in context: A294685 A200238 A368982 * A094127 A198924 A199605

Adjacent sequences: A254663 A254664 A254665 * A254667 A254668 A254669

Keyword

nonn,cons

Author

Roman Witula, Feb 04 2015

Extensions

a(99) corrected by Georg Fischer, Aug 12 2021

Status

approved