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%I #17 Nov 23 2024 19:37:55
%S 0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,
%T 1,0,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,
%U 1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0
%N The limit of the string "0, 1" under the operation 'append first k terms, increment k' with k=2 initially.
%C An infinite binary word.
%C Sum of the first 10^n terms b(n) begins: 0, 4, 43, 440, 4344, 43826, 439780, 4344256, 43430906, 435183414, 4378550493.
%H Paolo Xausa, <a href="/A215532/b215532.txt">Table of n, a(n) for n = 0..10011</a>
%e 01 -> 0101 -> 0101 010 -> 0101010 0101 -> 01010100101 01010 etc.
%t Module[{k = 1}, Nest[Join[#, #[[;; ++k]]] &, {0, 1}, 15]] (* _Paolo Xausa_, Nov 23 2024 *)
%o (Python)
%o TOP = 1000
%o a = [0]*TOP
%o a[1] = 1
%o n = k = 2
%o while n+k < TOP:
%o a[n:] = a[:k]
%o n += k
%o k += 1
%o for k in range(n):
%o print(a[k], end=', ')
%Y Cf. A094186, A215531, A215530.
%K nonn,easy
%O 0
%A _Alex Ratushnyak_, Aug 15 2012