login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A324679 Starting at n, a(n) is the maximum positive position 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 k-th 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. 0
0, 0, 0, 0, 0, 0, 0, 3442, 0, 0, 0, 27, 28, 29, 0, 0, 84, 2368556, 0, 0, 638385, 0, 0, 0, 0, 3642394, 0, 0, 0, 464, 43807680, 2117461, 2117462, 2117463, 2117464, 0, 0, 0, 562491, 562492, 179, 0, 0, 1, 1007, 0, 104, 79, 80, 0, 0, 190, 0, 0, 0, 0, 1107, 1108 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
LINKS
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 the maximal positive point for which this happens, thus a(11)=27.
PROG
(Python)
#Sequences A324660-A324692 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([i for i in d['stuck'] if i >0 ])
CROSSREFS
Sequence in context: A031824 A254093 A254086 * A324680 A273341 A107537
KEYWORD
nonn
AUTHOR
David Nacin, Mar 10 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)