

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 kth 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
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OFFSET

0,5


LINKS

Table of n, a(n) for n=0..59.


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 A324660A324692 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

Cf. A228474, A324660A324692.
Sequence in context: A019960 A069527 A154492 * A155840 A056194 A200304
Adjacent sequences: A324683 A324684 A324685 * A324687 A324688 A324689


KEYWORD

nonn


AUTHOR

David Nacin, Mar 10 2019


STATUS

approved



