OFFSET
1,2
COMMENTS
It is not known if the positive root of x^x^x^x = 2 is a rational number and, in consequence, whether this sequence is finite or not.
REFERENCES
F. Engel, Entwicklung der Zahlen nach Stammbrüchen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmänner in Marburg, 1913, pp. 190-191.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..100
F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner 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
Wikipedia, Tetration, Open questions
EXAMPLE
1.44660143242986417459733398759766148...
MAPLE
Digits:= 500:
c:= solve(x^(x^(x^x))=2, x):
engel:= (r, n)-> `if`(n=0 or r=0, NULL, [ceil(1/r),
engel(r*ceil(1/r)-1, n-1)][]):
engel(evalf(c), 39);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 01 2013
STATUS
approved