OFFSET
1,4
COMMENTS
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(2) sequence.
LINKS
Muharem Avdispahić and Faruk Zejnulahi, An integer sequence with a divisibility property, Fibonacci Quarterly, Vol. 58:4 (2020), 321-333.
FORMULA
Conjecture: a(n) = floor(n/phi + 1/phi^3) - [n+2 = Fibonacci(2*j+1) for some j], where phi = (1+sqrt(5))/2 and [] is the Iverson bracket. - Jon E. Schoenfield, Nov 03 2023
MATHEMATICA
zlist={-1, 2, 4};
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+1]; , AppendTo[mlist, mlist[[n]]]; AppendTo[zlist, mlist[[n+1]]]; ]; ];
mlist=Drop[mlist, 1]; mlist
PROG
(Python)
z_list=[-1, 2, 4]
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+2)
else:
m_list.append(m_list[n])
z_list.append(m_list[n+1])
print(m_list[1:])
CROSSREFS
KEYWORD
nonn
AUTHOR
Zenan Sabanac, Nov 03 2023
STATUS
approved