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A225208
Engel expansion of the positive root of x^x^x^x = 2.
3
1, 3, 3, 52, 106, 260, 279, 334, 491, 536, 728, 1161, 5678, 15183, 41437, 189034, 281965, 1118629, 3473978, 32869874, 82525851, 159312757, 424570638, 472381891, 563118608, 579529452, 1426303902, 2330077798, 2991863700, 25850322702, 34547004920, 37294688664
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
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
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
Cf. A225134 (decimal expansion), A225153 (continued fraction).
Sequence in context: A265717 A292753 A268136 * A290567 A339758 A100065
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 01 2013
STATUS
approved