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A079878 a(1)=1, then a(n)=2*a(n-1) if 2*a(n-1)<=n, a(n)=2*a(n-1)-n otherwise.

%I A079878 #23 Jul 20 2015 19:24:56
%S A079878 1,2,1,2,4,2,4,8,7,4,8,4,8,2,4,8,16,14,9,18,15,8,16,8,16,6,12,24,19,8,
%T A079878 16,32,31,28,21,6,12,24,9,18,36,30,17,34,23,46,45,42,35,20,40,28,3,6,
%U A079878 12,24,48,38,17,34,7,14,28,56,47,28,56,44,19,38,5,10,20,40,5,10,20,40,1,2
%N A079878 a(1)=1, then a(n)=2*a(n-1) if 2*a(n-1)<=n, a(n)=2*a(n-1)-n otherwise.
%C A079878 a(A200087(n)) = n and a(m) <> n for m < A200087(n). [_Reinhard Zumkeller_, Nov 13 2011]
%H A079878 Reinhard Zumkeller, <a href="/A079878/b079878.txt">Table of n, a(n) for n = 1..10000</a>
%F A079878 a(n) = A064434(n)+1.
%F A079878 It seems that sum(k=1, n, a(k))/n^2 ->1/4
%t A079878 nxt[{n_,a_}]:={n+1,If[2a<=n+1,2a,2a-n-1]}; Transpose[NestList[nxt,{1,1},80]][[2]] (* _Harvey P. Dale_, Jul 20 2015 *)
%o A079878 (PARI) a=1; for(n=2,100,b=if(sign(2*a-n)-1,2*a,2*a-n); a=b; print1(b,","))
%o A079878 (Haskell)
%o A079878 a079878 n = a079878_list !! (n-1)
%o A079878 a079878_list = 1 : zipWith (\x n -> if x <= n then x else x - n)
%o A079878                            (map (* 2) a079878_list) [2..]
%o A079878 -- _Reinhard Zumkeller_, Nov 13 2011
%Y A079878 Cf. A200063 (fixed points), A064456 (positions of 1).
%K A079878 nonn
%O A079878 1,2
%A A079878 _Benoit Cloitre_, Feb 20 2003