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).

1, 1, 2, 4, 8, 17, 38, 88, 206, 497, 1212

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

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)

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