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David Nacin, <a href="/A324688/a324688_1.png">A324688(n)/A228474(n)</a>

David Nacin, <a href="/A324688/a324688.png">A324688(n)</a>

(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 sgn(x):

if x:

return x//abs(x)

return 0

#Actual sequence

def a(n):

d = trip(n)

return sum(sgn(i) for i in d['flee'])

Cf. A228474, A324660-A324684A324692. Equals A324687-A324686.

allocated for David NacinStarting at n, a(n) is the difference of the number of times we move away from zero from positive spots and the number of times we move away from zero from negative spots 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, -1, 0, -7, -6, 0, -78, -2, -1, 0, 3, -14, -13, -2, 0, 9, -54646, -3, -2, 8497, 0, -8, -5, -4, -172288, -3, -2, 0, 27, 1784552, 33920, 33921, 33922, 33923, -3, 0, 8, -3137, -3136, -3, -5, -4, -3, -82, 0, -15, -12, -11, -9, -8, -4, -7, -4, -3, 0, 36, 37

0,5

Cf. A228474, A324660-A324684. Equals A324687-A324686.

allocated

sign

David Nacin, Mar 10 2019

approved

editing

allocating

allocated

allocated for David Nacin

allocating

approved