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A324677
Starting at n, a(n) is the smallest distance from zero among all positions from which a spot must be revisited on the next move, or zero if no such positions exist, according to the following rules. On the k-th step (k=1,2,3,...) move a distance of k in the direction of zero. If the number landed on has been landed on before, move a distance of k away.
1
0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 27, 15, 14, 0, 0, 26, 12, 0, 0, 4, 0, 0, 0, 0, 34, 0, 0, 0, 34, 2, 1, 13, 1, 1, 0, 0, 5, 1, 3, 2, 1, 0, 1, 2, 0, 21, 23, 22, 21, 20, 19, 18, 0, 0, 0, 25, 26, 27, 1, 26, 1, 1, 1, 33, 0, 0, 4, 3, 2, 1, 1, 1, 39, 1, 0, 0, 0, 0
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)
#Sequences A324660-A324692 generated by manipulating this trip function
#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