#
#
# Written by Antti Karttunen (his-firstname.his-surname@gmail.com)
# at Feb 27 2006.
#
#


import re

def A007088(n):
  '''Converts n to binary form. Or equally: nth decimal number using no other digits than 0 and 1.'''
  if 0 == n: return(0)
  else: return((n%2)+10*A007088(n/2))

def A007089(n):
  '''Converts n to ternary form. Or equally: nth decimal number using no other digits than 0, 1 and 2.'''
  if 0 == n: return(0)
  else: return((n%3)+10*A007089(n/3))



def take(n,g):
  '''Returns a list composed of n next elements returned by generator g. Inspired by Haskell'''
  z = []
  if 0 == n: return(z)
  for x in g:
    z.append(x)
    if n > 1:
      n = n-1
    else:
      return(z)


def gen_A001477():
  '''The nonnegative integers.'''
  i = 0
  while i > -1:
    yield i
    i = i+1


def A048724(n): return(n^(2*n))

def A065621(n): return(A048724(n-1)-((-1)**n))


# Here the maximum recursion depth is overflown already at take(26,gen_A001477)
#
# def gen_A001477():
#   '''The nonnegative integers.'''
#   yield 0
#   for x in gen_A001477(): yield x+1



def get_binpat_generator(binpat):
  '''Returns a generator which generates integers whose binary expansion matches binpat (prepended with few zeros).'''
  binpatre = re.compile("^" + binpat + "$")
  def foo():
    for n in gen_A001477():
      if(binpatre.match("0000" + repr(A007088(n)))): yield n
  return(foo)
    

def get_ternpat_generator(ternpat):
  '''Returns a generator which generates integers whose ternary expansion matches ternpat (prepended with few zeros).'''
  ternpatre = re.compile("^" + ternpat + "$")
  def foo():
    for n in gen_A001477():
      if(ternpatre.match("0000" + repr(A007089(n)))): yield n
  return(foo)
    

# def gen_A048719():
#   '''Binary expansion matches ((0)*0011)*(0*).'''
#   for n in gen_A001477(): 
#     if re.compile("^((0)*0011)*(0*)$").match("00" + repr(A007088(n))): yield n


gen_A048715 = get_binpat_generator("((0)*001)*(0*)")
gen_A048716 = get_binpat_generator("((0)*00(1?)1)*(0*)")
gen_A048717 = get_binpat_generator("((0)*00(1*)11)*(0*)")
gen_A048718 = get_binpat_generator("((0)*0001)*(0*)")
gen_A048719 = get_binpat_generator("((0)*0011)*(0*)")

gen_A051382 = get_ternpat_generator("(0|1)*(02)?(0|1)*")