#!/bin/bash# Douglas Hofstadter's notorious "Q-series":# Q(1) = Q(2) = 1# Q(n) = Q(n - Q(n-1)) + Q(n - Q(n-2)), for n&gt;2# This is a "chaotic" integer series with strange and unpredictable behavior.# The first 20 terms of the series are:# 1 1 2 3 3 4 5 5 6 6 6 8 8 8 10 9 10 11 11 12 #  See Hofstadter's book, "Goedel, Escher, Bach: An Eternal Golden Braid",#+ p. 137, ff.LIMIT=100     # Number of terms to calculate.LINEWIDTH=20  # Number of terms printed per line.Q[1]=1        # First two terms of series are 1.Q[2]=1echoecho "Q-series [$LIMIT terms]:"echo -n "${Q[1]} "             # Output first two terms.echo -n "${Q[2]} "for ((n=3; n <= $LIMIT; n++))  # C-like loop conditions.do   # Q[n] = Q[n - Q[n-1]] + Q[n - Q[n-2]]  for n&gt;2#  Need to break the expression into intermediate terms,#+ since Bash doesn't handle complex array arithmetic very well.  let "n1 = $n - 1"        # n-1  let "n2 = $n - 2"        # n-2    t0=`expr $n - ${Q[n1]}`  # n - Q[n-1]  t1=`expr $n - ${Q[n2]}`  # n - Q[n-2]    T0=${Q[t0]}              # Q[n - Q[n-1]]  T1=${Q[t1]}              # Q[n - Q[n-2]]Q[n]=`expr $T0 + $T1`      # Q[n - Q[n-1]] + Q[n - Q[n-2]]echo -n "${Q[n]} "if [ `expr $n % $LINEWIDTH` -eq 0 ]    # Format output.then   #      ^ Modula operator  echo # Break lines into neat chunks.fidoneechoexit 0# This is an iterative implementation of the Q-series.# The more intuitive recursive implementation is left as an exercise.# Warning: calculating this series recursively takes a VERY long time.