A372398 Numbers occurring exactly twice in Hofstadter G/H-like sequence H_5 (A005376).

1, 6, 7, 9, 12, 16, 21, 26, 27, 32, 33, 35, 40, 41, 43, 46, 51, 52, 54, 57, 61, 66, 67, 69, 72, 76, 81, 86, 87, 89, 92, 96, 101, 106, 107, 112, 113, 115, 118, 122, 127, 132, 133, 138, 139, 141, 146, 147, 149, 152, 156, 161, 166, 167, 172, 173, 175, 180, 181

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

Cf. A005374, A005376.

Numbers occurring exactly twice in Hofstadter G/H like sequence H_k: A000291 (k=2), A005374 (k=3), A372397 (k=4), this sequence (k=5).

Sequence in context: A309961 A108595 A186079 * A022938 A048585 A169761

Adjacent sequences: A372395 A372396 A372397 * A372399 A372400 A372401

Keyword

nonn

Author

A.H.M. Smeets, Apr 29 2024

Status

approved