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%I #14 Jun 20 2021 02:46:28
%S 0,1,3,10,11,23,30,31,33,100,101,103,110,111,223,230,231,233,300,301,
%T 303,310,311,323,330,331,333,1000,1001,1003,1010,1011,1023,1030,1031,
%U 1033,1100,1101,1103,1110,1111,2223,2230,2231,2233,2300,2301,2303,2310,2311
%N Loxton-van der Poorten sequence: base-4 representation contains only -1, 0, +1, converted to ordinary base-4 digits 0,1,2,3.
%C Loxton and van der Poorten's morphism (see A344893), or the way -1 digits cause borrows, shows that this sequence is base 4 digit strings with no digit pair 12, 13, 20, or 21, and least significant digit not 2.
%C The least significant digit can be any of 0,1,3, then each successive higher digit has three choices: 0,1,3 above a 0 or 1, or 0,2,3 above a 2 or 3. This allows a(n) to be calculated by mapping from the ternary digits of n to these choices, from least to most significant digit.
%H Kevin Ryde, <a href="/A344892/b344892.txt">Table of n, a(n) for n = 0..6561</a>
%F a(n) = A007090(A006288(n)).
%o (PARI) a(n) = my(v=digits(n,3),prev=0); forstep(i=#v,1,-1, prev=(v[i]+=(v[i]>(prev<2)))); fromdigits(v);
%Y Cf. A006288 (decimal), A344893 (morphism), A007090 (base 4).
%K nonn,easy,base
%O 0,3
%A _Kevin Ryde_, Jun 01 2021