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A082499 Take a string of n x's and insert n-1 ^'s and n-1 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 (list; graph; refs; listen; history; text; internal format)



For n=9, 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}.


Table of n, a(n) for n=1..11.

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)


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: A112482 A193050 A107597 * A100131 A119685 A025276

Adjacent sequences:  A082496 A082497 A082498 * A082500 A082501 A082502




W. Edwin Clark and Wouter Meeussen, Apr 29 2003


Term 1212 added by Vladimir Reshetnikov, Oct 29 2011

a(1) added by Franklin T. Adams-Watters, Nov 03 2011



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Last modified December 11 07:34 EST 2019. Contains 329914 sequences. (Running on oeis4.)