

A324668


Starting at n, a(n) is the minimum positive point visited, or zero if no positive points are visited, 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.


0



0, 1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 1, 1, 4, 5, 1, 1, 3, 1, 1, 6, 1, 2, 1, 1, 5, 1, 7, 1, 1, 2, 3, 1, 1, 7, 8, 1, 1, 2, 3, 5, 6, 1, 1, 9, 1, 2, 1, 4, 1, 1, 7, 8, 1, 10, 1, 2, 3, 1, 2, 1, 1, 1, 9, 10, 11, 1, 1, 1, 4, 5, 6, 7, 1, 9, 1, 1, 12, 1, 2, 3, 4, 5, 6, 1
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OFFSET

0,4


LINKS

Table of n, a(n) for n=0..85.


EXAMPLE

For n=2, the points visited are 2,1,1,4,0. As 1 is the smaller of the two positive values, 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}
def minorzero(x):
if x:
return min(x)
return 0
#Actual sequence
def a(n):
d = trip(n)
return minorzero([i for i in d['spots'] if i > 0])


CROSSREFS

Cf. A228474, A324660A324692.
Sequence in context: A127704 A307662 A050873 * A128221 A327856 A175488
Adjacent sequences: A324665 A324666 A324667 * A324669 A324670 A324671


KEYWORD

nonn


AUTHOR

David Nacin, Mar 10 2019


STATUS

approved



