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A199880
Engel expansion of x value of the unique pairwise intersection on (0,1) of distinct order 5 power tower functions with parentheses inserted.
2
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
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 11 2011
STATUS
approved