r"""
Python module for OEIS sequence number A048991.

Write down the numbers 1, 2, 3, ... , but omit any number (such as 12
or 101) which has appeared as a string earlier in the sequence.

Examples of use.
-----------------------------------------------------------------------
>>> from a048991 import *
>>> print a048991_list(15)
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16]
>>> print a048991_offset
1
>>> for x in a048991_list_pairs(6):
...     print x
...
(1, 1)
(2, 2)
(3, 3)
(4, 4)
(5, 5)
(6, 6)
>>> print a048991_list_upto(10)
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
>>> print a048991(5)
5
-----------------------------------------------------------------------
"""

from itertools import islice, izip, takewhile, count

__all__ = ('a048991_offset', 'a048991_list', 'a048991_list_pairs', 'a048991_list_upto', 'a048991', 'a048991_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a048991_offset = offset = 1


def a048991_gen():
    """Generator function for OEIS sequence A048991."""
    st = ''
    for n in count(1):
        t = str(n)
        if st.find(t) == -1:
            st += t
            yield n

def a048991_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(a048991_gen(), n))

def a048991_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), a048991_gen()))

def a048991_list_upto(m):
    """Returns a list of all terms not exceeding m > 0."""
    if m < 1: raise ValueError, 'Input must be a positive integer'
    return list(takewhile(lambda t: t <= m, a048991_gen()))

def a048991(n):
    """Returns the term with index n >= 1; offset 1."""
    if n < offset: raise ValueError, 'Input must be an integer >= offset = ' + str(offset)
    return list(islice(a048991_gen(), n-offset, n-offset+1)).pop()