

A335847


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


0



7, 7, 9, 5, 4, 3, 3, 3, 6, 0, 0, 1, 6, 8, 7, 7, 3, 5, 0, 3, 2, 9, 8, 4, 5, 5, 0, 2, 4, 2, 0, 4, 1, 9, 0, 8, 0, 1, 4, 8, 8, 4, 6, 3, 6, 1, 5, 9, 2, 1, 0, 6, 0, 1, 1, 9, 2, 9, 5, 6, 0, 5, 0, 7, 4, 0, 1, 4, 5, 7, 8, 0, 3, 6, 0, 6, 7, 8, 8, 0, 4, 6, 2, 4, 0, 6, 0, 9, 6, 7, 6, 3, 0, 5, 0, 7, 6, 1, 2, 3, 3, 3, 1, 2, 3, 7, 5
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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 evenindexed terms of {x(n)} converge.


LINKS

Table of n, a(n) for n=0..106.
Rafik Zeraoulia, Does this a_n = ... have a finite limit?, Math Stackexchange


EXAMPLE

0.77954333600168773503298455024204190801488463615921...


MATHEMATICA

(* note that FullSimplify[1/Factorial[i]1/Factorial[i+1]] == i/Gamma[2 + i]
which is i/Factorial[1 + i] for integer i *)
sequence = Table[Fold[#2^#1 &, Table[i/(i + 1)!, {i, n, 1, 1}]], {n, 1, 15}];
ListLinePlot[N /@ sequence, PlotRange > {0, 1}]
N[sequence[[1]]]
N[sequence[[2]]]


PROG

(PARI) my(N=100, y=(N/(N+1)!)); forstep(n=N1, 1, 1, y = ((n/(n+1)!)^y)); y \\ Michel Marcus, Jul 05 2020


CROSSREFS

Cf. A328942.
Sequence in context: A182470 A157290 A021566 * A244649 A267040 A225961
Adjacent sequences: A335844 A335845 A335846 * A335848 A335849 A335850


KEYWORD

nonn,cons


AUTHOR

R Zeraoulia, Jun 26 2020


STATUS

approved



