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A367068
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a(n) = ((Sum_{i=1..n} A340510(i))-1)/(n+1).
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2
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0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 42, 42
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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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(1) sequence.
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LINKS
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FORMULA
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For n>2, a(n) = a(n-1) if a(n-1) <> A340510(k) (for k=1..n-1) and a(n) = a(n-1)+1=A340510(n)-n otherwise. (See Proposition 3.1. of Avdispahić and Zejnulahi in the link above).
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MAPLE
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%/(n+1) ;
end proc:
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MATHEMATICA
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zlist = {-1, 1, 3};
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]; , AppendTo[mlist, mlist[[n]]];
AppendTo[zlist, mlist[[n + 1]]]; ]; ];
mlist = Drop[mlist, 1]; mlist
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PROG
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(Python)
z_list=[-1, 1, 3]
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+1)
else:
m_list.append(m_list[n])
z_list.append(m_list[n+1])
print(m_list[1:])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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