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%I #18 Jan 22 2024 06:34:48
%S 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 17,18,19,19,20,20,21,22,22,23,23,24,25,25,26,27,27,28,28,29,30,30,31,
%U 31,32,33,33,34,35,35,36,36,37,38,38,39,40,40,41,41,42
%N a(n) = ((Sum_{i=1..n} A367067(i))-3)/(n+3).
%C 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 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 zlist = {-1, 3, 5};
%t mlist = {-1, 0, 1};
%t For[n = 3, n <= 101, n++,
%t If[MemberQ[zlist, mlist[[n]]], AppendTo[mlist, mlist[[n]] + 1];
%t AppendTo[zlist, mlist[[n + 1]] + n + 2];,
%t AppendTo[mlist, mlist[[n]]]; AppendTo[zlist, mlist[[n + 1]]];];];
%t mlist = Drop[mlist, 1]; mlist
%o (Python)
%o z_list=[-1, 3, 5]
%o m_list=[-1, 0, 1]
%o n=2
%o for n in range(2, 100):
%o if m_list[n] in z_list:
%o m_list.append(m_list[n] + 1)
%o z_list.append(m_list[n+1] + n+3)
%o else:
%o m_list.append(m_list[n])
%o z_list.append(m_list[n+1])
%o print(m_list[1:])
%Y Cf. A367067.
%Y Cf. A073869 (AZM(0)), A367068 (AZM(1)), A367066 (AZM(2)).
%K nonn
%O 1,4
%A _Zenan Sabanac_, Dec 17 2023
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