2,2

For n=9, largest value is x^(x^(x^(x^(x^6)))) and results from the 132-th tree {0,{0,{0,{{{{{{0,0},0},0},0},0},0}}}} or {1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0}.

F. Goebel and R. P. Nederpelt, The number of numerical outcomes of iterated powers, Amer. Math. Monthly, 80 (1971), 1097-1103.

R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis. Amer. Math. Monthly 80 (1973), 868-876.

For n = 4 there are 5 functions: f1(x) = ((x^x)^x)^x; f2(x) = (x^(x^x))^x; f3(x) = x^((x^x)^x); f4(x) = x^(x^(x^x)); f5(x) = (x^x)^(x^x); but only 4 different values when x = sqrt(2).

Cf. A003019, A000081, A002845, A003018, A082543.

Sequence in context: A089796 A112482 A107597 this_sequence A100131 A119685 A025276

Adjacent sequences: A082496 A082497 A082498 this_sequence A082500 A082501 A082502

nonn

Edwin Clark (eclark(AT)math.usf.edu) and Meeussen Wouter (wouter.meeussen(AT)pandora.be), Apr 29 2003