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A094186
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Taking a(1)=0 and a(2)=1, sequence (a(n))n>1 is defined as follows : letting w(k)=a(1)a(2)...a(k) and w(infinity)= limit k ->infinity a(1)a(2)w(1)w(2)...w(k) we have w(infinity)=a(1)a(2)a(3)a(4)...
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7
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0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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An infinite binary word.
A shorter definition: the limit of the string "0, 1" under the operation 'append first k terms, increment k' with k=1 initially.
Sums of the first 10^n terms are: 0, 4, 36, 358, 3576, 34908, 356258, 3621799, 35807401, 352047694, 3495167093. [Alex Ratushnyak, Aug 15 2012]
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LINKS
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FORMULA
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It seems that limit n ->infinity 1/n*sum(k=1, n, a(k)) = 0.34...
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EXAMPLE
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w(1)=0, w(2)=01, therefore a(1)a(2)w(1)w(2)=01001=a(1)a(2)a(3)a(4)a(5) and sequence begins : 0,1,0,0,1,...
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MAPLE
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S:= "01":
for k from 1 to 40 do
A:= cat(A, A[1..k])
od:
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PROG
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(Python)
TOP = 1000
a = [0]*TOP
a[1] = 1
n = 2
k = 1
while n+k < TOP:
a[n:] = a[:k]
n += k
k += 1
for k in range(n):
print(a[k], end=", ")
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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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