#! /usr/bin/env python3
#
def collatz_inverse ( nlist ):

#*****************************************************************************80
#
## collatz_inverse() returns the Collatz preimage of a list of integers.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    28 January 2025
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer nlist[*]: a list of integers.
#
#  Output:
#
#    integer Tnlist[*]: the Collatz preimages of the values in nlist.
#
  Tnlist = []
#
#  A even preimage of n is 2*n.
#
  for n in nlist:
    Tnlist.append ( 2 * n )
#
#  Sometimes, there is an odd preimage of n.
#
  for n in nlist:
    if ( n != 4 ):            # We don't want the preimage of 4, which is 1
      if ( n % 3 == 1 ):      # Is n of the form 3*s+1?
        s = ( n - 1 ) // 3    # If so, solve n = 3*s+1 for s
        if ( s % 2 == 1 ):    # If s is odd, it's a second preimage of n.
          Tnlist.append ( s )
#
#  Get the unique elements by turning the list into a set,
#  and then bringing it back as a list again.
#
  Tnlist = list ( set ( Tnlist ) )
#
#  Sort the list.
#
  Tnlist = sorted ( Tnlist )

  return Tnlist

def collatz_inverse_test ( ):

#*****************************************************************************80
#
## collatz_inverse_test() tests collatz_inverse().
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    10 October 2024
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'collatz_inverse_test():' )
  print ( '  collatz_inverse() computes the preimage of a set of' )
  print ( '  integers under the Collatz transformation.' )

  for step in range ( 0, 13 ):
      
    if ( step == 0 ):
      nlist = [ 2 ]
    else:
      nlist = collatz_inverse ( nlist )

    print ( nlist )

  return

if ( __name__ == "__main__" ):
  collatz_inverse_test ( )