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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.

%I A199880 #29 Feb 16 2025 08:33:16
%S A199880 3,4,8,12,15,33,70,4338,22062,46566,98091,255284,2715877,10855925,
%T A199880 150153128,10009347774,34679420772,43644678207,74587800101,
%U A199880 229110893125,233558717156,286861037311,299617642336,312870987050,1632483095154,31761226898013,66327161231576
%N A199880 Engel expansion of x value of the unique pairwise intersection on (0,1) of distinct order 5 power tower functions with parentheses inserted.
%C A199880 Cf. A006784 for definition of Engel expansion.
%D A199880 F. Engel, Entwicklung der Zahlen nach Stammbrüchen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmänner in Marburg, 1913, pp. 190-191.
%H A199880 F. Engel, <a href="/A006784/a006784.pdf">Entwicklung der Zahlen nach Stammbrüchen</a>, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmänner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.
%H A199880 P. Erdős and Jeffrey Shallit, <a href="http://www.numdam.org/item?id=JTNB_1991__3_1_43_0">New bounds on the length of finite Pierce and Engel series</a>, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.
%H A199880 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>
%H A199880 Wikipedia, <a href="https://en.wikipedia.org/wiki/Engel_expansion">Engel Expansion</a>
%H A199880 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%e A199880 0.42801103796472992390204...
%p A199880 f:= x-> (x^(x^x))^(x^x): g:= x-> x^(x^((x^x)^x)):
%p A199880 Digits:= 700:
%p A199880 xv:= fsolve(f(x)=g(x), x=0..0.99):
%p A199880 engel:= (r, n)-> `if`(n=0 or r=0, NULL, [ceil(1/r), engel(r*ceil(1/r)-1, n-1)][]):
%p A199880 engel(xv, 39);
%Y A199880 Cf. A199814 (decimal expansion), A199879 (continued fraction).
%K A199880 nonn
%O A199880 1,1
%A A199880 _Alois P. Heinz_, Nov 11 2011