

A324663


Starting at n, a(n) is the number of moves made away from zero 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 from zero instead.


1



0, 0, 1, 0, 9, 10, 0, 740, 2, 3, 0, 7, 48, 49, 2, 0, 39, 348242, 3, 4, 59273, 0, 12, 5, 6, 523146, 3, 4, 0, 177, 3533234, 241226, 241225, 241226, 241227, 3, 0, 28, 101615, 101614, 93, 5, 4, 5, 420, 0, 49, 34, 35, 23, 24, 84, 13, 4, 5, 0, 262, 261, 260, 221950
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OFFSET

0,5


LINKS

Table of n, a(n) for n=0..59.
David Nacin, A324663(n)/A228474(n)


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, hence a(2) = 1.


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}
#Actual sequence
def a(n):
d = trip(n)
return len(d['flee'])


CROSSREFS

Cf. A228474, A324660A324692
Sequence in context: A067450 A220450 A318147 * A109409 A262551 A160563
Adjacent sequences: A324660 A324661 A324662 * A324664 A324665 A324666


KEYWORD

nonn


AUTHOR

David Nacin, Mar 10 2019


STATUS

approved



