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%I #43 Sep 08 2022 08:45:11
%S 1,1,1,2,2,3,3,4,4,4,5,5,6,6,6,7,7,8,8,8,9,9,10,10,11,11,11,12,12,13,
%T 13,13,14,14,15,15,16,16,16,17,17,18,18,18,19,19,20,20,21,21,21,22,22,
%U 23,23,23,24,24,25,25,25,26,26,27,27,28,28,28,29,29,30,30,30,31,31,32,32
%N a(1)=1, a(n) = ceiling((n - a(a(n-1)))/2).
%C Partial sums of A004641. - _Reinhard Zumkeller_, Dec 05 2009
%C This sequence generates A004641; see comment at A004641. - _Clark Kimberling_, May 25 2011
%H Reinhard Zumkeller, <a href="/A088462/b088462.txt">Table of n, a(n) for n = 1..10000</a>
%H N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)
%F a(n) = floor((sqrt(2)-1)*n + 1/sqrt(2)).
%F a(1) = a(2) = 1; a(n) = n - a(n-1) - a(a(n-2)) for n > 2. - _Altug Alkan_, Jun 24 2017
%t Table[Floor[(Sqrt[2] - 1) n + 1 / Sqrt[2]], {n, 100}] (* _Vincenzo Librandi_, Jun 26 2017 *)
%o (Python)
%o l=[0, 1, 1]
%o for n in range(3, 101): l.append(n - l[n - 1] - l[l[n - 2]])
%o print(l[1:]) # _Indranil Ghosh_, Jun 24 2017, after _Altug Alkan_
%o (Magma) [Floor((Sqrt(2)-1)*n+1/Sqrt(2)): n in [1..100]]; // _Vincenzo Librandi_, Jun 26 2017
%Y Cf. A005206.
%Y The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A000201 as the parent: A000201, A001030, A001468, A001950, A003622, A003842, A003849, A004641, A005614, A014675, A022342, A088462, A096270, A114986, A124841. - _N. J. A. Sloane_, Mar 11 2021
%K nonn
%O 1,4
%A _Benoit Cloitre_, Nov 12 2003
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