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A346000 Lexicographically earliest sequence of nonnegative integers such that two distinct terms differ by at least 4 decimal digits.

%I A346000 #19 Jul 20 2021 15:35:15
%S A346000 0,1111,2222,3333,4444,5555,6666,7777,8888,9999,10123,11032,12301,
%T A346000 13210,14567,15476,16745,17654,20231,21320,22013,23102,24675,25764,
%U A346000 26457,27546,30312,31203,32130,33021,34756,35647,36574,37465
%N A346000 Lexicographically earliest sequence of nonnegative integers such that two distinct terms differ by at least 4 decimal digits.
%C A346000 This is the distance 4 lexicode over the decimal alphabet.
%H A346000 J. H. Conway, <a href="https://doi.org/10.1016/0012-365X(90)90008-6">Integral lexicographic codes</a>, Discrete Mathematics 83.2-3 (1990): 219-235.
%H A346000 J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1109/TIT.1986.1057187">Lexicographic codes: error-correcting codes from game theory</a>, IEEE Transactions on Information Theory, 32:337-348, 1986.
%p A346000 # Hamming distance in base b
%p A346000 Hammdist:=proc(m,n,b) local t1,t2,L1,L2,L,d,i;
%p A346000 t1:=convert(m,base,b); L1:=nops(t1);
%p A346000 t2:=convert(n,base,b); L2:=nops(t2); L:=L1;
%p A346000 if L2<L1 then for i from 1 to L1-L2 do t2:=[op(t2),0]; od;
%p A346000 elif L1<L2 then for i from 1 to L2-L1 do t1:=[op(t1),0]; od; L:=L2;
%p A346000 fi;
%p A346000 d:=0;
%p A346000 for i from 1 to L do if t1[i]<>t2[i] then d:=d+1; fi; od;
%p A346000 d; end;
%p A346000 # Build lexicode with min distance D in base b, search up to M
%p A346000 # C = size of code found, tooc = 1 means too close to code
%p A346000 unprotect(D);
%p A346000 lexicode := proc(D,b,M) local cod,v,i,tooc,C;
%p A346000 cod:=[0]; C:=1;
%p A346000 # can we add v ?
%p A346000 for v from 0 to M do
%p A346000    tooc:=-1;
%p A346000    for i from 1 to C do
%p A346000    if Hammdist(v,cod[i],b)<D then tooc:=1; break; fi;
%p A346000                      od:
%p A346000 if tooc = -1 then C:=C+1; cod:=[op(cod),v]; fi;
%p A346000 od:
%p A346000 cod;
%p A346000 end;
%Y A346000 Lexicodes of minimal distance 1,2,3,... over alphabets of size 2: A001477, A001969, A075926, A075928, A075931, A075934, ...; size 3: A001477, A346002, A346003; size 10: A001477, A343444, A333568, A346000, A346001.
%K A346000 nonn,base
%O A346000 1,2
%A A346000 _N. J. A. Sloane_, Jul 20 2021