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A079411 a(1)=1, a(n) = n - a(a(ceiling(n/2))).

%I A079411 #17 Sep 08 2022 08:45:08
%S A079411 1,1,2,3,4,5,5,6,6,7,7,8,9,10,10,11,12,13,14,15,16,17,17,18,19,20,20,
%T A079411 21,22,23,24,25,25,26,26,27,27,28,29,30,30,31,31,32,33,34,34,35,35,36,
%U A079411 36,37,38,39,39,40,40,41,42,43,43,44,44,45,46,47,47,48,49,50,51,52,53,54
%N A079411 a(1)=1, a(n) = n - a(a(ceiling(n/2))).
%H A079411 Robert Israel, <a href="/A079411/b079411.txt">Table of n, a(n) for n = 1..10000</a>
%F A079411 a(n) is asymptotic to n*(sqrt(3)-1); conjecture: (a(n)-n*(sqrt(3)-1))/log(n) is bounded.
%p A079411 f:= proc(n) option remember;
%p A079411   n - procname(procname(ceil(n/2)))
%p A079411 end proc:
%p A079411 f(1):= 1:
%p A079411 seq(f(n),n=1..100); # _Robert Israel_, Oct 24 2017
%t A079411 Fold[Append[#1, #2 - #1[[#1[[Ceiling[#2/2] ]] ]] ] &, {1}, Range[2, 74]] (* _Michael De Vlieger_, Oct 24 2017 *)
%o A079411 (PARI) a(n)=if(n<2,1,n-a(a(ceil(n/2))))
%o A079411 (Magma) [n eq 1 select 1 else n-Self(Self(Ceiling(n/2))): n in [1..80]]; // _Vincenzo Librandi_, Oct 25 2017
%Y A079411 Cf. A076895.
%K A079411 nonn
%O A079411 1,3
%A A079411 _Benoit Cloitre_, Feb 16 2003