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#!/usr/bin/bc

scale = 20
phi = (1 + sqrt(5)) / 2
loglimit = 1000 - 1 + l(sqrt(5))/l(10)

scale = 0
n = 1
min = -1
max = -1
while (1) {
    print n, " (", min, ", ", max, ")\n"
    scale = 20
    if (l(phi^n - (1 - phi)^n)/l(10) > loglimit) {
        max = n
    } else {
        min = n
    }
    scale = 0
    if (max - min == 1) {
        max
        halt
    }
    if (max == -1) {
        n *= 2
    } else {
        n = (max + min) / 2
    }
}