A345656 Decimal expansion of the abscissa of the minimum of log(x)*log(1+x).

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

Offset

0,1

Comments

The function f(x)=log(x)*log(1+x) is zero at x=0 and zero at x=1, and attains a local minimum at x=0.318...

This constant equals the zero of the first derivative, i.e., it satisfies (1+x)*log(1+x) + x*log(x) = 0.

Links

Table of n, a(n) for n=0..86.

Example

Equals 0.3183657369410991840261143... The ordinate value is -0.31634671137020605439495...

Maple

Digits := 100 ; fsolve( (1+x)*log(1+x)+x*log(x)) ;

Mathematica

RealDigits[x /. FindRoot[(1 + x)*Log[1 + x] + x*Log[x], {x, 1}, WorkingPrecision -> 120], 10, 100][[1]] (* Amiram Eldar, Jun 23 2021 *)

Prog

(PARI) solve(x=0.3, 0.4, x*log(x)+(1+x)*log(1+x)) \\ M. F. Hasler, Jun 23 2021

Crossrefs

Sequence in context: A322428 A130300 A366873 * A308742 A065451 A178148

Adjacent sequences: A345653 A345654 A345655 * A345657 A345658 A345659

Keyword

nonn,cons

Author

R. J. Mathar, Jun 21 2021

Status

approved