

A324685


Starting at n, a(n) is the difference of the number of times we revisit spots coming from positive spots and the number of times we revisit spots coming from negative spots 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, 0, 0, 0, 0, 0, 21, 0, 0, 0, 1, 5, 5, 0, 0, 3, 7429, 0, 0, 1852, 0, 0, 0, 0, 28253, 0, 0, 0, 3, 267870, 6225, 6226, 6227, 6228, 0, 0, 2, 598, 597, 2, 1, 0, 1, 9, 0, 2, 2, 2, 3, 3, 0, 2, 0, 0, 0, 8, 8, 8, 6462, 6461, 6460, 6459, 6458
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OFFSET

0,8


LINKS

Table of n, a(n) for n=0..63.
David Nacin, A324685
David Nacin, A324685(n)/A228474(n)


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(sgn(i) for i in d['stuck'])


CROSSREFS

Cf. A228474, A324660A324692. Equals A324684A324683.
Sequence in context: A259331 A209614 A167263 * A224114 A110454 A265156
Adjacent sequences: A324682 A324683 A324684 * A324686 A324687 A324688


KEYWORD

sign


AUTHOR

David Nacin, Mar 10 2019


STATUS

approved



