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A082499
Take a string of n x's and insert n-1 ^'s and n-2 pairs of parentheses in all possible legal ways. Sequence gives number of distinct values when x = sqrt(2).
10
1, 1, 2, 4, 8, 17, 38, 88, 206, 497, 1212
OFFSET
1,3
COMMENTS
For n=10, largest value is x^(x^(x^(x^(x^6)))) and results from the 132nd 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}.
LINKS
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 (8) (1973), 868-876.
R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis (annotated cached copy)
EXAMPLE
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).
CROSSREFS
KEYWORD
nonn,more,changed
AUTHOR
EXTENSIONS
Term 1212 added by Vladimir Reshetnikov, Oct 29 2011
a(1) added by Franklin T. Adams-Watters, Nov 03 2011
STATUS
approved