

A324680


Starting at n, a(n) is the largest distance from zero among all positions from which a spot must be revisited on the next move, or zero if no such positions exist, 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.


2



0, 0, 0, 0, 0, 0, 0, 3442, 0, 0, 0, 27, 140, 139, 0, 0, 84, 3072845, 0, 0, 638385, 0, 0, 0, 0, 4869724, 0, 0, 0, 464, 43807680, 2117461, 2117462, 2117463, 2117464, 0, 0, 24, 696919, 696918, 179, 1, 0, 1, 1920, 0, 148, 86, 85, 84, 83, 190, 63, 0, 0, 0, 1107
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,8


LINKS

Table of n, a(n) for n=0..56.
David Nacin, A324680
David Nacin, A324680(n)/A228474(n)


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. The only position from which we are forced to revisit a spot is 27, which forces a return to 51. Since this is the only time this happens it is also has the largest distance from zero, thus a(11)=27.


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 maxorzero(x):
if x:
return max(x)
return 0
#Actual sequence
def a(n):
d=trip(n)
return maxorzero([abs(i) for i in d['stuck']])


CROSSREFS

Cf. A228474, A324660A324692.
Sequence in context: A254093 A254086 A324679 * A273341 A107537 A260500
Adjacent sequences: A324677 A324678 A324679 * A324681 A324682 A324683


KEYWORD

nonn


AUTHOR

David Nacin, Mar 10 2019


STATUS

approved



