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A324686
Starting at n, a(n) is the number of times we move away from zero from a negative position 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, 1, 0, 8, 8, 0, 409, 2, 2, 0, 2, 31, 31, 2, 0, 15, 201444, 3, 3, 25388, 0, 10, 5, 5, 347717, 3, 3, 0, 75, 874341, 103653, 103652, 103652, 103652, 3, 0, 10, 52376, 52375, 48, 5, 4, 4, 251, 0, 32, 23, 23, 16, 16, 44, 10, 4, 4, 0, 113, 112, 111, 129093
OFFSET
0,5
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. Of these, we move away from zero at -7, -19, 13, 12, 31, 51, and 27. Two of these are negative and thus a(11)=2.
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 sgn(x):
if x:
return x//abs(x)
return 0
#Actual sequence
def a(n):
d = trip(n)
return sum(1 for i in d['flee'] if i<0)
CROSSREFS
KEYWORD
nonn
AUTHOR
David Nacin, Mar 10 2019
STATUS
approved