Natural Numbers Stream

natural-sequence.py

#!/usr/bin/python
# Copyright (c) 2010 Willington Vega, http://wvega.com/
# Licensed under WTFPL (http://sam.zoy.org/wtfpl/)

class NaturalSequence:
    def __init__(self, digit, length=None):
        """Creates a stream to generate natural numbers whose first digit is self.digit.
        if length is given only numbers of that length will be generated"""
        self.digit = digit
        self.length = length
        self.maxp = length and (10 ** (length - 1))
        self.stream = []

        # the distance between the digit and the next natural number that 
        # starts with digit. 
        # Ex: a(1) = 9 then 1 + 9 = 10; a(2) = 18 then 2 + 18 = 20 and so on...
        self.a = 9 * digit

        # the prepartion step...
        if length is None:
            self.current = digit - 1
            # p = 10^(m-1); m is the length of the numbers been generated in a given time
            self.p = 1
            # how much numbers remaining before have to increase the length of 
            # the numbers been generated
            self.k = 1
        else:
            self.p = self.maxp
            # there is 1 number of length 1, 10 numbers of length 2, 
            # 100 numbers of length 3 ... 10^(m-1) numbers of length m,
            # that start with self.digit 
            self.k = self.p
            self.current = (self.digit * self.p) - 1

    def next(self, n=1):
        """returns n next numbers of the sequence"""

        if self.maxp and self.p > self.maxp:
            return None

        numbers = []
        for i in range(0,n):
            # there are no reamining numbers of length log(self.p)
            if self.k <= 0:
                # (self.p * (self.a - 1)) is the amount of numbers (less 1) 
                # that DON't start with self.digit before the next number 
                # that starts with self.digit
                self.current = self.current + (self.p * (self.a - 1))
                # the length of the numbers has been increased by 1
                self.p = self.p * 10   
                self.k = self.p

                if self.maxp and self.p > self.maxp:
                    break
            # get the next number
            self.current = self.current + 1
            # consume one number
            self.k = self.k - 1
            numbers.append(self.current)

        self.stream = self.stream + numbers

        if numbers is None or len(numbers) == 0:
            return None
        elif n == 1:
            return numbers[0]
        return numbers

natural = NaturalSequence(3)
print "The first 20 natural numbers that start with digit 3"
print natural.next(10)
print natural.next(10)