#!/usr/bin/env python
# -*- coding: utf-8 -*-

# Stéganô - Stéganô is a basic Python Steganography module.
# Copyright (C) 2010-2017  Cédric Bonhomme - https://www.cedricbonhomme.org
#
# For more information : https://github.com/cedricbonhomme/Stegano
#
# 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/>

__author__ = "Cedric Bonhomme"
__version__ = "$Revision: 0.2 $"
__date__ = "$Date: 2011/12/28 $"
__revision__ = "$Date: 2012/12/14 $"
__license__ = "GPLv3"

import math
import itertools

def identity():
    """
    f(x) = x
    """
    n = 0
    while True:
        yield n
        n += 1

def Dead_Man_Walking():
    n = 0
    while True:
        yield n + 7
        n += 2

def OEIS_A000217():
    """
    http://oeis.org/A000217
    Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n.
    """
    n = 0
    while True:
        yield (n*(n+1))//2
        n += 1

def fermat():
    """
    Generate the n-th Fermat Number.
    """
    y = 5
    while True:
        yield y
        y = pow(y-1,2)+1

def mersenne():
    """
    Generate 2^n-1.
    """
    y = 1
    while True:
        yield y
        y = 2*y + 1

def eratosthenes():
    """
    Generate the prime numbers with the sieve of Eratosthenes.
    """
    d = {}
    for i in itertools.count(2):
        if i in d:
            for j in d[i]:
                d[i + j] = d.get(i + j, []) + [j]
            del d[i]
        else:
            d[i * i] = [i]
            yield i

def eratosthenes_composite():
    """
    Generate the composite numbers with the sieve of Eratosthenes.
    """
    p1 = 3
    for p2 in eratosthenes():
        for n in range(p1 + 1, p2):
            yield n
        p1 = p2

def carmichael():
    for m in eratosthenes_composite():
        for a in range(2, m):
            if pow(a,m,m) != a:
                break
        else:
            yield m

def ackermann(m, n):
    """
    Ackermann number.
    """
    if m == 0:
        return n + 1
    elif n == 0:
        return ackermann(m - 1, 1)
    else:
        return ackermann(m - 1, ackermann(m, n - 1))

def fibonacci():
    """
    A generator for Fibonacci numbers, goes to next number in series on each call.
    This generator start at 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, ...
    See: http://oeis.org/A000045
    """
    a, b = 1, 2
    while True:
        yield a
        a, b = b, a + b

def syracuse(l=15):
    """
    Generate the sequence of Syracuse.
    """
    y = l
    while True:
        yield y
        q,r = divmod(y,2)
        if r == 0:
            y = q
        else:
            y = 3*y + 1

def log_gen():
    """
    Logarithmic generator.
    """
    y = 1
    while True:
        adder = max(1, math.pow(10, int(math.log10(y))))
        yield int(y)
        y = y + adder

if __name__ == "__main__":
    # Point of entry in execution mode.
    f = fibonacci()
    for x in range(13):
        #print(next(f), end=' ') # 0 1 1 2 3 5 8 13 21 34 55 89 144
        pass