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A324678 Starting at n, a(n) is the minimum negative 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, -3165, 0, 0, 0, 0, -140, -139, 0, 0, 0, -3072845, 0, 0, -383171, 0, 0, 0, 0, -4869724, 0, 0, 0, -217, -31071367, -1854085, -1854084, -1854083, -1854082, 0, 0, -24, -696919, -696918, -26, -1, 0, 0, -1920, 0, -148, -86, -85, -84, -83, -144 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..51.

EXAMPLE

For n=41, the points visited are 41, 40, 38, 35, 31, 26, 20, 13, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, 11, -10, 12, -11, -35, -60, -34, -61, -33, -62, -32, -1, -33, 0. The only position from which we are forced to revisit a spot is -1 which forces a return to -33. As this is the only position and it is negative, it is the minimum negative position and thus a(41)=-1.

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 minorzero(x):

if x:

return min(x)

return 0

#Actual sequence

def a(n):

d=trip(n)

return minorzero([i for i in d['stuck'] if i<0])

CROSSREFS

Cf. A228474, A324660-A324692.

Sequence in context: A151750 A031610 A252636 * A068266 A140350 A309024

Adjacent sequences: A324675 A324676 A324677 * A324679 A324680 A324681

KEYWORD

sign

AUTHOR

David Nacin, Mar 10 2019

STATUS

approved

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Last modified November 26 14:22 EST 2022. Contains 358362 sequences. (Running on oeis4.)