|
| |
|
|
A367065
|
|
a(1)=2, thereafter a(n) is the least positive integer not yet in the sequence such that Sum_{i=1..n} a(i) == 2 (mod n+2).
|
|
2
|
|
|
|
2, 4, 1, 7, 9, 3, 12, 14, 5, 17, 6, 20, 22, 8, 25, 27, 10, 30, 11, 33, 35, 13, 38, 40, 15, 43, 16, 46, 48, 18, 51, 19, 54, 56, 21, 59, 61, 23, 64, 24, 67, 69, 26, 72, 74, 28, 77, 29, 80, 82, 31, 85, 32, 88, 90, 34, 93, 95, 36, 98, 37, 101, 103, 39, 106, 108, 41, 111, 42, 114
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
This is the Avdispahić-Zejnulahi sequence AZ(2). For a positive integer k, the Avdispahić-Zejnulahi sequence AZ(k) is given by: a(1)=k, thereafter a(n) is the least positive integer not yet in the sequence such that Sum_{i=1..n} a(i) == k (mod n+k). It is interesting to note that (AZ(k)) represents a sequence of permutations of the set of positive integers. (See Links section for details concerning AZ(1).)
|
|
|
LINKS
|
|
|
|
MATHEMATICA
|
lst={2}; f[s_List]:=Block[{k=1, len=3+Length@lst, t=Plus@@lst}, While[MemberQ[s, k]||Mod[k+t, len]!=2, k++]; AppendTo[lst, k]]; Nest[f, lst, 100]
|
|
|
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(z_list[1:])
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
