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A372397
Numbers occurring exactly twice in Hofstadter G/H-like sequence H_4 (A005375).
2
1, 5, 6, 8, 11, 15, 19, 20, 24, 25, 27, 31, 32, 34, 37, 41, 42, 44, 47, 51, 55, 56, 58, 61, 65, 69, 70, 74, 75, 77, 80, 84, 88, 89, 93, 94, 96, 100, 101, 103, 106, 110, 114, 115, 119, 120, 122, 126, 127, 129, 132, 136, 137, 139, 142, 146, 150, 151, 155, 156
OFFSET
1,2
COMMENTS
Also first prepending column of the 4-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
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 < 50:
if nn == 0:
Hno = H(nn, 4)
else:
Hnn = H(nn, 4)
if Hnn == Hno:
n += 1
print(Hnn, end = ", ")
Hno = Hnn
nn += 1
CROSSREFS
Numbers occurring exactly twice in Hofstadter G/H like sequence H_k: A000291 (k=2), A005374 (k=3), this sequence (k=4), A372398 (k=5).
Sequence in context: A332549 A091091 A262161 * A290744 A120151 A022937
KEYWORD
nonn,more
AUTHOR
A.H.M. Smeets, Apr 29 2024
STATUS
approved