A367068 -id:A367068 - cp's OEIS frontend

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

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, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 41, 42

Offset: 1

Zenan Sabanac, Dec 17 2023

nonn

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.

Muharem Avdispahić and Faruk Zejnulahi, An integer sequence with a divisibility property, Fibonacci Quarterly, Vol. 58:4 (2020), 321-333.

Cf. A367067.

Cf. A073869 (AZM(0)), A367068 (AZM(1)), A367066 (AZM(2)).

zlist = {-1, 3, 5};
mlist = {-1, 0, 1};
For[n = 3, n <= 101, n++,
  If[MemberQ[zlist, mlist[[n]]], AppendTo[mlist, mlist[[n]] + 1];
    AppendTo[zlist, mlist[[n + 1]] + n + 2];,
    AppendTo[mlist, mlist[[n]]]; AppendTo[zlist, mlist[[n + 1]]];];];
mlist = Drop[mlist, 1]; mlist

z_list=[-1, 3, 5]
m_list=[-1, 0, 1]
n=2
for n in range(2, 100):
    if m_list[n] in z_list:
        m_list.append(m_list[n] + 1)
        z_list.append(m_list[n+1] + n+3)
    else:
        m_list.append(m_list[n])
        z_list.append(m_list[n+1])
print(m_list[1:])

cp's OEIS Frontend

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

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