#!/usr/bin/env python3

# Powerful digit counts

# =====================

# Problem 63

# The 5-digit number, :math:`16807=7^5`, is also a fifth power. Similarly, the 9-digit

# number, :math:`134217728=8^9`, is a ninth power.

#

# How many n-digit positive integers exist which are also an nth power?

# .. rubric:: Solution

# .. py:module:: euler62

# :synopsis: Cubic permutations

# Use the :py:func:`euler04.digits` function.

from euler04 import digits

# Yield a sequence of triples with a number, i, power, p, and :math:`i^p`

# where the length of :math:`i^p` == p.

# What's the upper bound on this search?

# For what p does this no longer work?

# When p ≥ 22, it appears that :math:`i^p` no longer produces numbers of p digits.

def genNdigitNPower( limit=30 ):

i += 1

# Test the module components.

def test():

import doctest

doctest.testmod(verbose=0)

# Compute the answer.

def answer():

return len( list( genNdigitNPower(30) ) )

# Confirm the answer.

def confirm(ans):

assert ans == 49, "{0!r} Incorrect".format(ans)

# Create some output.

if __name__ == "__main__":

test()

ans= answer()

confirm(ans)

print( "The number of n-digit positive integers exist which are also an nth power:", ans )