OFFSET
0,5
EXAMPLE
For n=2, the points visited are 2,1,-1,-4,0 with the move from -4 to 0 being the only one to the right, hence a(2)=1.
PROG
(Python)
#spots - positions in order with possible repetition
#flee - positions from which we move away from zero with possible repetition
#stuck - positions from which we move to a spot already visited with possible repetition
def trip(n):
stucklist = list()
spotsvisited = [n]
leavingspots = list()
turn = 0
forbidden = {n}
while n != 0:
turn += 1
sign = n // abs(n)
st = sign * turn
if n - st not in forbidden:
n = n - st
else:
leavingspots.append(n)
if n + st in forbidden:
stucklist.append(n)
n = n + st
spotsvisited.append(n)
forbidden.add(n)
return {'stuck':stucklist, 'spots':spotsvisited,
'turns':turn, 'flee':leavingspots}
#Actual sequence
def a(n):
d=trip(n)
return sum(1 for i in range(d['turns']) if d['spots'][i+1] > d['spots'][i])
CROSSREFS
KEYWORD
nonn
AUTHOR
David Nacin, Mar 10 2019
STATUS
approved