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A324661
Starting at n, a(n) is the total number of moves made to the left 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, 1, 3, 2, 14, 15, 3, 864, 8, 9, 4, 15, 64, 65, 10, 5, 62, 390904, 13, 14, 66452, 6, 29, 18, 19, 610401, 15, 16, 7, 218, 4434563, 266008, 266007, 266008, 266009, 17, 8, 51, 106681, 106680, 128, 21, 20, 21, 505, 9, 77, 60, 61, 46, 47, 110, 35, 22, 23, 10, 327
OFFSET
0,3
EXAMPLE
For n=2, the points visited are 2,1,-1,-4,0 with the moves from 2 to 1, 1 to -1, and -1 to -4 being the only ones to the left, hence a(2)=3.
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}
#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