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A050136 a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1), otherwise a(n)=5*n.

%I A050136 #25 Oct 15 2019 11:52:07
%S A050136 1,10,5,2,25,12,6,3,45,22,11,60,30,15,7,80,40,20,95,47,23,110,55,27,
%T A050136 13,130,65,32,16,8,4,160,165,82,41,180,90,190,195,97,48,24,215,107,53,
%U A050136 26,235,117,58,29,14,260,265,132,66,33,285,142,71,35,17,310,155,77,38,19,9,340,170,85,42,21
%N A050136 a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1), otherwise a(n)=5*n.
%C A050136 Does this sequence contain every positive integer exactly once?
%H A050136 Robert Israel, <a href="/A050136/b050136.txt">Table of n, a(n) for n = 1..10000</a>
%p A050136 S:= {0,1}: A[1]:= 1:
%p A050136 for n from 2 to 100 do
%p A050136   v:= floor(A[n-1]/2);
%p A050136   if not member(v,S) then A[n]:= v
%p A050136   else A[n]:= 5*n
%p A050136   fi;
%p A050136   S:= S union {A[n]};
%p A050136 od:
%p A050136 seq(A[i],i=1..100); # _Robert Israel_, Aug 07 2018
%t A050136 f[s_List] := Block[{len = Length@s, m = Floor[s[[-1]]/2]}, Append[s, If[MemberQ[s, m], 5 len, m]]]; Rest@ Nest[f, {0, 1}, 65] (* _Robert G. Wilson v_, Aug 07 2018 *)
%Y A050136 Cf. A050000, A050128, A050132, A050135.
%K A050136 nonn,look
%O A050136 1,2
%A A050136 _Clark Kimberling_
%E A050136 Corrected by _Robert Israel_, Aug 07 2018