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 A094186 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)... 7
 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)
 OFFSET 1,1 COMMENTS 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] LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA It seems that limit n ->infinity 1/n*sum(k=1, n, a(k)) = 0.34... EXAMPLE 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,... MAPLE S:= "01": for k from 1 to 40 do A:= cat(A, A[1..k]) od: seq(parse(A[i]), i=1..length(A)); # Robert Israel, Mar 28 2019 PROG (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=", ") # Alex Ratushnyak, Aug 15 2012 CROSSREFS Cf. A164349, A215531, A215532. Sequence in context: A270742 A373338 A164349 * A267371 A285205 A286654 Adjacent sequences: A094183 A094184 A094185 * A094187 A094188 A094189 KEYWORD nonn AUTHOR Benoit Cloitre, May 07 2004 STATUS approved

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Last modified July 12 16:40 EDT 2024. Contains 374251 sequences. (Running on oeis4.)