OFFSET
0,8
LINKS
EXAMPLE
For n=11, the points visited are 11, 10, 8, 5, 1, -4, 2, -5, 3, -6, 4, -7, -19, -32, -18, -3, 13, 30, 12, 31, 51, 72, 50, 27, 51, 26, 0. The only position from which we are forced to revisit a spot is 27, which forces a return to 51. Since this is the only position for which this happens, it is the closest position to zero where this happens and thus a(11)=27.
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}
def minorzero(x):
if x:
return min(x)
return 0
#Actual sequence
def a(n):
d=trip(n)
return minorzero([abs(i) for i in d['stuck']])
CROSSREFS
KEYWORD
nonn
AUTHOR
David Nacin, Mar 10 2019
STATUS
approved