OFFSET
1,2
COMMENTS
Also first prepending column of the 5-Zeckendorf array (see Ericksen and Anderson).
N. J. A. Sloane observed already the relation between Hofstadter G/H-like sequences H_k and k-Zeckendorf arrays in May 2003, at least for k = 3 (see formula section and history of A005374). First observation most probably by Diego Torres, Nov 2002, relating the Hofstadter G/H-like sequences H_k with the k-Zeckendorf arrays and Lamé sequences of order k (see comments in A005375 and A005376).
LINKS
A.H.M. Smeets, Table of n, a(n) for n = 1..20000
Larry Ericksen and Peter G. Anderson, Patterns in differences between rows in k-Zeckendorf arrays, The Fibonacci Quarterly, Vol. 50, February 2012.
PROG
(Python)
def H(n, k):
if n == 0:
return 0
else:
i, x = 0, n-1
while i < k:
i, x = i+1, H(x, k)
return n-x
n, nn = 0, 0
while n < 59:
if nn == 0:
Hno = H(nn, 5)
else:
Hnn = H(nn, 5)
if Hnn == Hno:
n += 1
print(Hnn, end = ", ")
Hno = Hnn
nn += 1
CROSSREFS
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Apr 29 2024
STATUS
approved