A328941 Decimal expansion of lim_{n->infinity} (1 - 1/2)^((1/2 - 1/3)^(...^(1/(2n-1) - 1/(2n)))).

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

Offset

0,1

Comments

The sequence of real values x(n) = (1 - 1/2)^((1/2 - 1/3)^(...^(1/n - 1/(n+1)))) converges to two different limits depending on whether n is even or odd. This integer sequence gives the decimal expansion of the lower limit, to which the odd-indexed terms of {x(n)} converge.

Links

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

Zeraoulia Rafik, Question on Math Stackexchange

Example

0.56778606544394002098000796382530333102219963214865...

Prog

(PARI) my(N=99, y=(1/(N*(N+1)))); forstep(n=N-1, 1, -1, y=1/(n*(n+1))^y); y \\ Michel Marcus, Nov 08 2019

Crossrefs

Cf. A328942.

Sequence in context: A095942 A139395 A029911 * A205691 A002141 A367150

Adjacent sequences: A328938 A328939 A328940 * A328942 A328943 A328944

Keyword

nonn,cons

Author

R Zeraoulia, Oct 31 2019

Extensions

More terms from Jon E. Schoenfield, Nov 02 2019

Status

approved