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A169956 Lexicographically earliest sequence with positive integers satisfying a(a(n)) = 2*n+2.

%I A169956 #99 Jul 14 2022 22:54:29
%S A169956 2,4,5,6,8,10,9,12,16,14,13,18,24,22,17,20,32,26,21,34,40,30,25,28,48,
%T A169956 38,29,50,56,46,33,36,64,42,37,66,72,54,41,44,80,70,45,82,88,62,49,52,
%U A169956 96,58,53,98,104,78,57,60,112,102,61,114,120,94,65,68,128,74
%N A169956 Lexicographically earliest sequence with positive integers satisfying a(a(n)) = 2*n+2.
%C A169956 Previous name was: Similar to A080653, but without the "monotonically increasing sequence" condition.
%C A169956 Sequence contains all the even numbers and odd numbers k such that k mod 4 = 1. - _Yifan Xie_, Jul 05 2022
%H A169956 Yifan Xie, <a href="/A169956/b169956.txt">Table of n, a(n) for n = 1..10000</a>
%F A169956 From _Yifan Xie_, Jul 05 2022: (Start)
%F A169956 a(A169957(n)-1) = 2*n for n > 1.
%F A169956 a(4*n-1) = 4*n+1 for n >= 1.
%F A169956 a(4*n+1) = 8*n for n >= 1. (End)
%e A169956 For n=3, a(3) must satisfy a(a(3)) = 2*3+2 = 8. If a(3) = 0, we get 8 = a(a(3)) = a(0) = 1, so a(3) > 0. Using the same method twice we get a(3) > 2. If a(3) = 3, hence 3 = a(3) = a(a(3)) = 8, so a(3) > 3. If a(3) = 4, using a(2) = 4 we get 8 = a(a(3)) = a(4) = 2*2+2 = 6, so a(3) > 4. If a(3) = 5, there are no conflicts using the definition, so a(3) = 5. - _Yifan Xie_, Jul 05 2022
%Y A169956 Cf. A080653, A079905, A169957.
%K A169956 nonn,easy,look
%O A169956 1,1
%A A169956 _Eric Angelini_, Aug 02 2010
%E A169956 New name and more terms from _Yifan Xie_, Jul 05 2022
%E A169956 a(23) corrected by _Yifan Xie_, Jul 05 2022