A324684 - OEIS

A324684

Starting at n, a(n) is the number of times we move from a positive spot to a spot we have already visited 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, 31, 0, 0, 0, 1, 1, 1, 0, 0, 3, 25871, 0, 0, 6154, 0, 0, 0, 0, 30429, 0, 0, 0, 9, 422464, 25055, 25055, 25056, 25057, 0, 0, 0, 9685, 9685, 5, 0, 0, 1, 20, 0, 3, 1, 1, 0, 0, 5, 0, 0, 0, 0, 17, 17, 17, 15244, 15244, 15245, 15246, 15247, 1, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,8

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

For n=43, the points visited are 43, 42, 40, 37, 33, 28, 22, 15, 7, -2, 8, -3, 9, -4, 10, -5, 11, -6, 12, -7, 13, -8, 14, -9, -33, -58, -32, -59, -31, -60, -30, 1, 33, 0. The only time we revisit a spot is when we move from 1 to 33. As this only occurs for one positive number, a(43)=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}

#Actual sequence

def a(n):

d = trip(n)

return sum(1 for i in d['stuck'] if i > 0)

CROSSREFS

Cf. A228474, A324660-A324692.

Sequence in context: A140762 A028363 A091511 * A213070 A221432 A085012

Adjacent sequences: A324681 A324682 A324683 * A324685 A324686 A324687

KEYWORD

nonn

AUTHOR

David Nacin, Mar 10 2019

STATUS

approved