r"""
Python module for OEIS sequence number A019460.

Add 1, multiply by 1, add 2, multiply by 2, and so on.

Examples of use.
-----------------------------------------------------------------------
>>> from a019460 import *
>>> print a019460_list(14)
[2, 3, 3, 5, 10, 13, 39, 43, 172, 177, 885, 891, 5346, 5353]
>>> print a019460_offset
0
>>> for x in a019460_list_pairs(6):
...     print x
...
(0, 2)
(1, 3)
(2, 3)
(3, 5)
(4, 10)
(5, 13)
>>> print a019460(5)
13
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count

__all__ = ('a019460_offset', 'a019460_list', 'a019460_list_pairs', 'a019460', 'a019460_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a019460_offset = offset = 0

def a019460_gen(start):
    """Generator function for OEIS sequence A019460."""
    x = start
    for m in count(1):
        yield x
        x += m
        yield x
        x *= m

def a019460_list(n):
    """Returns a list of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(islice(a019460_gen(2), n))

def a019460_list_pairs(n):
    """Returns a list of tuples (n, a(n)) of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(izip(xrange(offset, n+offset), a019460_gen(2)))

def a019460(n):
    """Returns the term with index n >= 0; offset 0."""
    if n < offset: raise ValueError, 'Input must be an integer >= offset = ' + str(offset)
    return list(islice(a019460_gen(2), n-offset, n-offset+1)).pop()