OFFSET
1,7
COMMENTS
T(1,0) = 0 is defined in order to make the triangle of numbers regular.
T(n,k) = 1 whenever k is a power of 3 and k>1.
LINKS
Pontus von Brömssen, Rows n = 1..32, flattened
EXAMPLE
Triangle begins:
n\k 0 1 2 3 4 5 6 7 8 9 10 11
---------------------------------------------------------------
1: 0
2: 1 1
3: 1 1 0
4: 12 1 2 1
5: 28 1 0 1 2
6: 64 1 2 1 2 4
7: 60 4 2 1 4 0 2
8: 54 1 2 1 62 16 2 48
9: 2 1 0 1 0 0 0 0 0
10: 80 40 4 1 20 2000 60 72 4 1
11: 40 20 5 1 85 240 5 5 20 1 320
12: 1260 128 2 1 272 4 2 48 68 1 20 1440
T(10,0) = 80, because A243845 eventually enters a cycle of length 80.
PROG
(Python)
from sympy.ntheory.factor_ import digits
from functools import reduce
def drop(x, n, k):
# Drop all digits k from x in base n.
return reduce(lambda x, j:n*x+j if j!=k else x, digits(x, n)[1:], 0)
def cycle_length(n, k, m):
# Brent's algorithm for finding cycle length.
# Note: The function may hang if the sequence never enters a cycle.
if (m, n, k)==(5, 10, 7):
return 0 # A little cheating; see A335506.
p=1
length=0
tortoise=hare=1
nz=0
while True:
hare=drop(m*hare, n, k)
while hare and hare%n==0:
hare//=n
nz+=1 # Keep track of the number of trailing zeros.
length+=1
if tortoise==hare:
break
if p==length:
tortoise=hare
nz=0
p*=2
length=0
return length if not nz else 0
def A335503(n, k):
return cycle_length(n, k, 3) if n>1 else 0
CROSSREFS
KEYWORD
AUTHOR
Pontus von Brömssen, Jun 13 2020
STATUS
approved