#  ramanujan.py -- Compute the N:th Ramanujan number
#  
#  Copyright (C) 2018-2021 Mikael Djurfeldt
#
#  This program is free software; you can redistribute it and/or modify
#  it under the terms of the GNU General Public License as published by
#  the Free Software Foundation; either version 3 of the License, or
#  (at your option) any later version.
#
#  This program is distributed in the hope that it will be useful,
#  but WITHOUT ANY WARRANTY; without even the implied warranty of
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#  GNU General Public License for more details.
#
#  You should have received a copy of the GNU General Public License
#  along with this program.  If not, see <http://www.gnu.org/licenses/>.
#

# Version 2

# return the N:th Ramanujan number (sum of two cubes in more than one way)
#
def ramanujan (n):
    w = 0 # Ramanujan number candidate
    b0 = 1 # first second term to try
    while n > 0:
        w += 1 # try next candidate

        # increase initial b0 until 1 + b0^3 >=w
        while 1 + b0 * b0 * b0 < w:
            b0 += 1
            
        a = 1
        a3 = 1
        b = b0
        b3 = b0 * b0 * b0
        count = 0 # number of ways to write w
        while a <= b:
            s = a3 + b3
            if s < w:
                a += 1 # if sum is too small, increase a
                a3 = a * a * a
            elif s == w:
                count += 1 # found a sum!
                if count > 1:
                    n -= 1
                    break
                b -= 1 # increase b both if sum too large and to find next way to write w
                b3 = b * b * b
            else:
                b -= 1 
                b3 = b * b * b
                
    return w

print (ramanujan (21))