A215832 Decimal expansion of the maximum of the function f(x) = log(cos(sin(x)))/log(sin(cos(x))), x in (0,Pi/2).

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

Offset

0,1

Comments

The inverse of this maximum is equal to A215833. The argument z in (0,Pi/2) for which f(z) = max{f(x): x in (0,Pi/2)} is given in A168546. We note that f is increasing in the interval (0,z) and decreasing in the interval (z,Pi/2).

Links

Table of n, a(n) for n=0..124.

Roman Wituła, Danuta Jama, Edyta Hetmaniok, and Damian Słota, On some inequality of the trygonometric type, Zeszyty Naukowe Politechniki Slaskiej - Matematyka-Fizyka (Science Fascicle of Silesian Technical University - Math.-Phys.), 92 (2010), 83-92.

Example

We have M := max{f(x): x in (0,Pi/2)} = 0.64101923763280082467982344748964716145889051447774...

Mathematica

RealDigits[Maximize[Log[Cos[Sin[x]]]/Log[Sin[Cos[x]]], {x}, WorkingPrecision -> 130][[1]]][[1]] (* Amiram Eldar, Mar 27 2026 *)

Prog

(PARI) f(x) = log(cos(sin(x)))/log(sin(cos(x)));
f(solve(r = 4/5, 1, derivnum(x = r, f(x)))) \\ Amiram Eldar, Mar 27 2026

Crossrefs

Cf. A215833, A168546, A215670, A215668, A216891.

Sequence in context: A365955 A368831 A158567 * A021160 A391709 A354887

Adjacent sequences: A215829 A215830 A215831 * A215833 A215834 A215835

Keyword

nonn,cons

Author

Roman Witula, Aug 24 2012

Extensions

a(12) onward corrected by Amiram Eldar, Mar 27 2026

Status

approved