r""" Python module for OEIS sequence number A105391. Numbers m such that there is an equal number of numbers <= m that are contained and that are not contained in the concatenation of terms <= m in A048991. Examples of use. ----------------------------------------------------------------------- >>> from a105391 import * >>> print a105391_list(6) [740, 1260, 1262, 5230, 15804, 15814] >>> print a105391_offset 1 >>> for x in a105391_list_pairs(6): ... print x ... (1, 740) (2, 1260) (3, 1262) (4, 5230) (5, 15804) (6, 15814) >>> print a105391(3) 1262 ----------------------------------------------------------------------- """ from itertools import islice, izip, count __all__ = ('a105391_offset', 'a105391_list', 'a105391_list_pairs', 'a105391', 'a105391_gen') __author__ = 'Nick Hobson <nickh@qbyte.org>' a105391_offset = offset = 1 def a105391_gen(): """Generator function for OEIS sequence A105391.""" st, c = '', 0 for n in count(1): t = str(n) if st.find(t) == -1: st += t c += 1 if c == n - c: yield n def a105391_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(a105391_gen(), n)) def a105391_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), a105391_gen())) def a105391(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(a105391_gen(), n-offset, n-offset+1)).pop()