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A335504 Triangle read by rows, 0 <= k < n, n >= 1: T(n,k) is the eventual period of the sequence x(j) (or 0 if x(j) never enters a cycle) defined as follows: x(0) = 1 and for j > 1 x(j) is obtained from 4*x(j-1) by deleting all occurrences of the digit k in base n.

%I A335504 #13 Jul 11 2020 08:53:39
%S A335504 0,1,1,2,1,1,1,1,0,0,2,24,2,2,1,16,18,1,6,1,42,33,1,1,15,1,24,3,3,1,1,
%T A335504 0,1,0,0,0,3,1,195,27,1,465,147,2,6,1002,18,4,42,1,66,2,10,10,738,
%U A335504 1660,25,5,180,1,2,15,35,150,4,1490
%N A335504 Triangle read by rows, 0 <= k < n, n >= 1: T(n,k) is the eventual period of the sequence x(j) (or 0 if x(j) never enters a cycle) defined as follows: x(0) = 1 and for j > 1 x(j) is obtained from 4*x(j-1) by deleting all occurrences of the digit k in base n.
%C A335504 T(1,0) = 0 is defined in order to make the triangle of numbers regular.
%C A335504 T(n,k) = 1 whenever k is a power of 4 and k>1.
%H A335504 Pontus von Brömssen, <a href="/A335504/b335504.txt">Rows n = 1..32, flattened</a>
%e A335504 Triangle begins:
%e A335504    n\k   0    1    2    3    4    5    6    7    8    9
%e A335504   -----------------------------------------------------
%e A335504    1:    0
%e A335504    2:    1    1
%e A335504    3:    2    1    1
%e A335504    4:    1    1    0    0
%e A335504    5:    2   24    2    2    1
%e A335504    6:   16   18    1    6    1   42
%e A335504    7:   33    1    1   15    1   24    3
%e A335504    8:    3    1    1    0    1    0    0    0
%e A335504    9:    3    1  195   27    1  465  147    2    6
%e A335504   10: 1002   18    4   42    1   66    2   10   10  738
%o A335504 (Python)
%o A335504 from sympy.ntheory.factor_ import digits
%o A335504 from functools import reduce
%o A335504 def drop(x,n,k):
%o A335504   # Drop all digits k from x in base n.
%o A335504   return reduce(lambda x,j:n*x+j if j!=k else x,digits(x, n)[1:],0)
%o A335504 def cycle_length(n,k,m):
%o A335504   # Brent's algorithm for finding cycle length.
%o A335504   # Note: The function may hang if the sequence never enters a cycle.
%o A335504   if (m,n,k)==(5,10,7):
%o A335504     return 0 # A little cheating; see A335506.
%o A335504   p=1
%o A335504   length=0
%o A335504   tortoise=hare=1
%o A335504   nz=0
%o A335504   while True:
%o A335504     hare=drop(m*hare,n,k)
%o A335504     while hare and hare%n==0:
%o A335504       hare//=n
%o A335504       nz+=1 # Keep track of the number of trailing zeros.
%o A335504     length+=1
%o A335504     if tortoise==hare:
%o A335504       break
%o A335504     if p==length:
%o A335504       tortoise=hare
%o A335504       nz=0
%o A335504       p*=2
%o A335504       length=0
%o A335504   return length if not nz else 0
%o A335504 def A335504(n,k):
%o A335504   return cycle_length(n,k,4) if n>1 else 0
%Y A335504 Cf. A335502, A335503, A335505, A335506.
%Y A335504 Cf. A243846, A306569, A306773.
%K A335504 nonn,base,tabl
%O A335504 1,4
%A A335504 _Pontus von Brömssen_, Jun 13 2020