A199880 Engel expansion of x value of the unique pairwise intersection on (0,1) of distinct order 5 power tower functions with parentheses inserted.

3, 4, 8, 12, 15, 33, 70, 4338, 22062, 46566, 98091, 255284, 2715877, 10855925, 150153128, 10009347774, 34679420772, 43644678207, 74587800101, 229110893125, 233558717156, 286861037311, 299617642336, 312870987050, 1632483095154, 31761226898013, 66327161231576

Offset

1,1

Comments

Cf. A006784 for definition of Engel expansion.

References

F. Engel, Entwicklung der Zahlen nach Stammbrüchen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmänner in Marburg, 1913, pp. 190-191.

Links

Table of n, a(n) for n=1..27.

F. Engel, Entwicklung der Zahlen nach Stammbrüchen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmänner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.

P. Erdős and Jeffrey Shallit, New bounds on the length of finite Pierce and Engel series, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.

Eric Weisstein's World of Mathematics, Engel Expansion

Wikipedia, Engel Expansion

Index entries for sequences related to Engel expansions

Example

0.42801103796472992390204...

Maple

f:= x-> (x^(x^x))^(x^x): g:= x-> x^(x^((x^x)^x)):
Digits:= 700:
xv:= fsolve(f(x)=g(x), x=0..0.99):
engel:= (r, n)-> `if`(n=0 or r=0, NULL, [ceil(1/r), engel(r*ceil(1/r)-1, n-1)][]):
engel(xv, 39);

Crossrefs

Cf. A199814 (decimal expansion), A199879 (continued fraction).

Sequence in context: A022432 A271474 A120116 * A063227 A293462 A190158

Adjacent sequences: A199877 A199878 A199879 * A199881 A199882 A199883

Keyword

nonn

Author

Alois P. Heinz, Nov 11 2011

Status

approved