A372398 -id:A372398 - cp's OEIS frontend

A372397 Numbers occurring exactly twice in Hofstadter G/H-like sequence H_4 (A005375).

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

A.H.M. Smeets, Apr 29 2024

nonn

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).

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.

Cf. A005374, A005375.

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).

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

cp's OEIS Frontend

A372397 Numbers occurring exactly twice in Hofstadter G/H-like sequence H_4 (A005375).

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