A367066 a(n) = ((Sum_{i=1..n} A367065(i))-2)/(n+2).

0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 42, 43

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

Table of n, a(n) for n=1..70.

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

Cf. A367065.

Sequence in context: A086335 A123387 A123070 * A057361 A136409 A039729

Adjacent sequences: A367063 A367064 A367065 * A367067 A367068 A367069

Keyword

nonn

Author

Zenan Sabanac, Nov 03 2023

Status

approved