cp's OEIS Frontend

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

%I A372397 #35 Feb 02 2025 13:00:03
%S A372397 1,5,6,8,11,15,19,20,24,25,27,31,32,34,37,41,42,44,47,51,55,56,58,61,
%T A372397 65,69,70,74,75,77,80,84,88,89,93,94,96,100,101,103,106,110,114,115,
%U A372397 119,120,122,126,127,129,132,136,137,139,142,146,150,151,155,156
%N A372397 Numbers occurring exactly twice in Hofstadter G/H-like sequence H_4 (A005375).
%C A372397 Also first prepending column of the 4-Zeckendorf array (see Ericksen and Anderson).
%C A372397 _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).
%H A372397 A.H.M. Smeets, <a href="/A372397/b372397.txt">Table of n, a(n) for n = 1..20000</a>
%H A372397 Larry Ericksen and Peter G. Anderson, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/50-1/EricksenAnderson.pdf">Patterns in differences between rows in k-Zeckendorf arrays</a>, The Fibonacci Quarterly, Vol. 50, February 2012.
%o A372397 (Python)
%o A372397 def H(n,k):
%o A372397     if n == 0:
%o A372397         return 0
%o A372397     else:
%o A372397         i, x = 0, n-1
%o A372397         while i < k:
%o A372397             i, x = i+1, H(x,k)
%o A372397         return n-x
%o A372397 n, nn = 0, 0
%o A372397 while n < 50:
%o A372397     if nn == 0:
%o A372397         Hno = H(nn,4)
%o A372397     else:
%o A372397         Hnn = H(nn,4)
%o A372397         if Hnn == Hno:
%o A372397             n += 1
%o A372397             print(Hnn, end = ", ")
%o A372397         Hno = Hnn
%o A372397     nn += 1
%Y A372397 Cf. A005374, A005375.
%Y A372397 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).
%K A372397 nonn
%O A372397 1,2
%A A372397 _A.H.M. Smeets_, Apr 29 2024