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In computer science, the iterated logarithm of n {\displaystyle n} , written log* n {\displaystyle n} , is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1 {\displaystyle 1}. The simplest formal definition is the result of this recurrence relation:
On the positive real numbers, the continuous super-logarithm is essentially equivalent:
i.e. the base b iterated logarithm is log ∗ n = y {\displaystyle \log ^{*}n=y} if n lies within the interval y − 1 b < n ≤ y b {\displaystyle ^{y-1}b The iterated logarithm accepts any positive real number and yields an integer. Graphically, it can be understood as the number of "zig-zags" needed in Figure 1 to reach the interval {\displaystyle } on the x-axis.