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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)
 OFFSET 1,3 COMMENTS 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}. 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 Cf. A003019, A000081, A002845, A003018, A082543. Sequence in context: A112482 A193050 A107597 * A100131 A119685 A025276 Adjacent sequences:  A082496 A082497 A082498 * A082500 A082501 A082502 KEYWORD nonn,more AUTHOR W. Edwin Clark and Wouter Meeussen, Apr 29 2003 EXTENSIONS Term 1212 added by Vladimir Reshetnikov, Oct 29 2011 a(1) added by Franklin T. Adams-Watters, Nov 03 2011 STATUS approved

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