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A367069 a(n) = ((Sum_{i=1..n} A367067(i))-3)/(n+3).

%I A367069 #18 Jan 22 2024 06:34:48
%S A367069 0,1,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,10,11,12,12,13,14,14,15,15,16,17,
%T A367069 17,18,19,19,20,20,21,22,22,23,23,24,25,25,26,27,27,28,28,29,30,30,31,
%U A367069 31,32,33,33,34,35,35,36,36,37,38,38,39,40,40,41,41,42
%N A367069 a(n) = ((Sum_{i=1..n} A367067(i))-3)/(n+3).
%C A367069 For a positive integer k define the Avdispahić-Zejnulahi sequence AZ(k) by b(1)=k, and thereafter b(n) is the least positive integer not yet in the sequence such that Sum_{i=1..n} b(i) == k (mod n+k). Define the Avdispahić-Zejnulahi means sequence AZM(k) by a(n) = ((Sum_{i=1..n} b(i))-k)/(n+k). This is the AZM(3) sequence.
%H A367069 Muharem Avdispahić and Faruk Zejnulahi, <a href="https://www.researchgate.net/publication/341726940_AN_INTEGER_SEQUENCE_WITH_A_DIVISIBILITY_PROPERTY">An integer sequence with a divisibility property</a>, Fibonacci Quarterly, Vol. 58:4 (2020), 321-333.
%t A367069 zlist = {-1, 3, 5};
%t A367069 mlist = {-1, 0, 1};
%t A367069 For[n = 3, n <= 101, n++,
%t A367069   If[MemberQ[zlist, mlist[[n]]], AppendTo[mlist, mlist[[n]] + 1];
%t A367069     AppendTo[zlist, mlist[[n + 1]] + n + 2];,
%t A367069     AppendTo[mlist, mlist[[n]]]; AppendTo[zlist, mlist[[n + 1]]];];];
%t A367069 mlist = Drop[mlist, 1]; mlist
%o A367069 (Python)
%o A367069 z_list=[-1, 3, 5]
%o A367069 m_list=[-1, 0, 1]
%o A367069 n=2
%o A367069 for n in range(2, 100):
%o A367069     if m_list[n] in z_list:
%o A367069         m_list.append(m_list[n] + 1)
%o A367069         z_list.append(m_list[n+1] + n+3)
%o A367069     else:
%o A367069         m_list.append(m_list[n])
%o A367069         z_list.append(m_list[n+1])
%o A367069 print(m_list[1:])
%Y A367069 Cf. A367067.
%Y A367069 Cf. A073869 (AZM(0)), A367068 (AZM(1)), A367066 (AZM(2)).
%K A367069 nonn
%O A367069 1,4
%A A367069 _Zenan Sabanac_, Dec 17 2023