#!/usr/bin/perl
# Copyright 2004 by Richard Mansfield Kandarian
# This program is licensed under the GPL. The GPL text is available at
# http://www.opensource.org/licenses/gpl-license.php

$sum1 = $sum2 = 2;
for $n (2..$ARGV[0]-1){
  $dn = $n+1; $t = 1 + 2*$n/$dn;
  $sum1 += $t; $sum2 += $t;
  my $d = 1/$n + 1/($dn);
  my $m = 2;
  my $c = 1;
  my $nc;
  my $m = sqrt($n*($n - 1)/(2*$n - 1));
  $m += .5;
  $m =~ s/\..*$//;
  my $c1 = $d*($m - 1) + 1/$m;
  my $c2 = $d*($m) + 1/($m + 1);
  if($c2 < $c1){
    $m++;
    $c = $c2;
  }else{
    $c = $c1;
  }
  if($c < 1){
    $sum2 -= 1 - $c;
  }
  printf("%6s: %20s, % 3.6s, %3s, %20s, % 3.6s\n",
    $n+1, $sum1, $sum1/($n+1), $m, $sum2, $sum2/($n+1));
}