r""" Python module for OEIS sequence number A123483. Second order Recaman's sequence: a(0) = 0; for n > 0, a(n) = a(n-1) - A005132(n) if that number is positive and not already in the sequence, otherwise a(n-1) + A005132(n). Examples of use. ----------------------------------------------------------------------- >>> from a123483 import * >>> print a123483_list(16) [0, 1, 4, 10, 8, 15, 2, 22, 34, 13, 24, 46, 36, 59, 50, 26] >>> print a123483_offset 0 >>> for x in a123483_list_pairs(6): ... print x ... (0, 0) (1, 1) (2, 4) (3, 10) (4, 8) (5, 15) >>> print a123483(3) 10 ----------------------------------------------------------------------- """ from itertools import islice, izip, count from a005132 import a005132_gen __all__ = ('a123483_offset', 'a123483_list', 'a123483_list_pairs', 'a123483', 'a005132_gen') __author__ = 'Nick Hobson <nickh@qbyte.org>' a123483_offset = offset = 0 def a123483_list(n): """Returns a list of the first n >= 0 terms of OEIS sequence A123483.""" if n < 0: raise ValueError, 'Input must be a non-negative integer' return list(islice(a005132_gen(a005132_gen(count())), n)) def a123483_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), a005132_gen(a005132_gen(count())))) def a123483(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(a005132_gen(a005132_gen(count())), n-offset, n-offset+1)).pop()