r""" Python module for OEIS sequence number A128333. a(0) = 0; for n > 0, a(n) = a(n-1)/2 if that number is an integer and not already in the sequence, otherwise a(n) = 3*a(n-1) + 1. Examples of use. ----------------------------------------------------------------------- >>> from a128333 import * >>> print a128333_list(16) [0, 1, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5] >>> print a128333_offset 0 >>> for x in a128333_list_pairs(6): ... print x ... (0, 0) (1, 1) (2, 4) (3, 2) (4, 7) (5, 22) >>> print a128333(3) 2 ----------------------------------------------------------------------- """ from itertools import islice, izip, count __all__ = ('a128333_offset', 'a128333_list', 'a128333_list_pairs', 'a128333', 'a128333_gen') __author__ = 'Nick Hobson <nickh@qbyte.org>' a128333_offset = offset = 0 def a128333_gen(): """Generator function for OEIS sequence A128333.""" s, x = set(), 0 while True: yield x s.add(x) x = x/2 if x%2 == 0 and x/2 not in s else 3*x + 1 def a128333_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(a128333_gen(), n)) def a128333_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), a128333_gen())) def a128333(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(a128333_gen(), n-offset, n-offset+1)).pop()