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A360585 The integers of the sequence appear exactly twice. Between the two copies of k there are k even integers. The sequence is always extended with the smallest integer not leading to a contradiction.

%I A360585 #16 Mar 01 2023 14:41:16
%S A360585 1,2,1,3,4,5,6,2,3,7,8,9,10,4,5,11,12,13,14,6,15,16,7,17,18,19,20,8,9,
%T A360585 21,22,23,24,10,25,26,11,27,28,29,30,12,13,31,32,33,34,14,35,36,15,37,
%U A360585 38,39,40,16,17,41,42,43,44,18,19,45,46,47,48,20,49,50
%N A360585 The integers of the sequence appear exactly twice. Between the two copies of k there are k even integers. The sequence is always extended with the smallest integer not leading to a contradiction.
%e A360585 There is one even integer between the two 1s: this is the integer 2;
%e A360585 there are two even integers between the two 2s: they are 4 and 6;
%e A360585 there are three even integers between the two 3s: they are 4, 6 and 2; etc.
%t A360585 lst={1};k=2;
%t A360585 Do[While[FreeQ[lst,k]&&Count[lst[[First@@Position[lst,t]+1;;]],a_/;EvenQ@a]!=t,AppendTo[lst,k];k++];lst=AppendTo[lst,t],{t,25}];lst (* _Giorgos Kalogeropoulos_, Feb 28 2023 *)
%Y A360585 Cf. A360476.
%K A360585 nonn
%O A360585 1,2
%A A360585 _Eric Angelini_, Feb 12 2023
%E A360585 More terms from _Jinyuan Wang_, Feb 14 2023