function [ n_data, n, p ] = pi_values ( n_data )

%*****************************************************************************80
%
%% pi_values() returns values of the Pi function.
%
%  Discussion:
%
%    Pi[n] is the number of primes less than or equal to n.
%
%    In Mathematica, the function can be evaluated by:
%
%      PrimePi[n]
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    19 September 2004
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Stephen Wolfram,
%    The Mathematica Book,
%    Fourth Edition,
%    Wolfram Media / Cambridge University Press, 1999.
%
%  Input:
%
%    integer N_DATA.  The user sets N_DATA to 0 before the first call.  
%    Thereafter, it should simply be the value returned by the previous call.
%
%  Output:
%
%    integer N_DATA.  On each call, the routine increments N_DATA by 1, and
%    returns the corresponding data; when there is no more data, the
%    output value of N_DATA will be 0 again.
%
%    integer N, the argument.
%
%    integer P, the value of the function.
%
  n_max = 17;

  n_vec = [ ...
            10, ...
            20, ...
            30, ...
            40, ...
            50, ...
            60, ...
            70, ...
            80, ...
            90, ...
           100, ...
          1000, ...
         10000, ...
        100000, ...
       1000000, ...
      10000000, ...
     100000000, ...
    1000000000 ];

  p_vec = [ ...
             4, ...
             8, ...
            10, ...
            12, ...
            15, ...
            17, ...
            19, ...
            22, ...
            24, ...
            25, ...
           168, ...
          1229, ...
          9592, ...
         78498, ...
        664579, ...
       5761455, ...
      50847534 ];

  if ( n_data < 0 )
    n_data = 0;
  end

  n_data = n_data + 1;

  if ( n_max < n_data )
    n_data = 0;
    n = 0;
    p = 0;
  else
    n = n_vec(n_data);
    p = p_vec(n_data);
  end

  return
end
