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A324664
Starting at n, a(n) is the smallest distance from zero for which the next move is a step away from zero, or zero if no such move is ever made, 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 from zero instead.
1
0, 0, 1, 0, 3, 1, 0, 5, 4, 1, 0, 7, 6, 1, 4, 0, 7, 8, 7, 1, 2, 0, 5, 4, 1, 2, 7, 1, 0, 13, 2, 1, 10, 1, 1, 7, 0, 5, 1, 3, 2, 1, 10, 1, 2, 0, 17, 16, 1, 14, 1, 2, 11, 10, 1, 0, 1, 1, 17, 1, 15, 1, 1, 1, 11, 10, 0, 4, 1, 2, 1, 1, 1, 15, 1, 13, 1, 1, 0, 2, 1, 1
OFFSET
0,5
EXAMPLE
For n=2, the points visited are 2,1,-1,-4,0 with all moves being towards zero from the current position except for the move from -1 to -4. Thus the closest distance to zero from which a move is made away from zero is a(2) = 1.
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['flee']])
CROSSREFS
KEYWORD
nonn
AUTHOR
David Nacin, Mar 10 2019
STATUS
approved