A328942 Decimal expansion of lim_{n->infinity} (1 - 1/2)^((1/2 - 1/3)^(...^(1/(2n) - 1/(2n+1)))).

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

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 upper limit, to which the even-indexed terms of {x(n)} converge.

Links

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

Zeraoulia Rafik, Question on Math Stackexchange

Example

0.85885772008416606762434379473241623070938618180813.....

Prog

(PARI) my(N=100, 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. A328941.

Sequence in context: A021542 A336058 A198136 * A308743 A305582 A144454

Adjacent sequences: A328939 A328940 A328941 * A328943 A328944 A328945

Keyword

nonn,cons

Author

R Zeraoulia, Oct 31 2019

Extensions

More terms from Jon E. Schoenfield, Nov 02 2019

Status

approved