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A346000 Lexicographically earliest sequence of nonnegative integers such that two distinct terms differ by at least 4 decimal digits. 5
0, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 10123, 11032, 12301, 13210, 14567, 15476, 16745, 17654, 20231, 21320, 22013, 23102, 24675, 25764, 26457, 27546, 30312, 31203, 32130, 33021, 34756, 35647, 36574, 37465 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is the distance 4 lexicode over the decimal alphabet.

LINKS

Table of n, a(n) for n=1..34.

J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235.

J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Transactions on Information Theory, 32:337-348, 1986.

MAPLE

# Hamming distance in base b

Hammdist:=proc(m, n, b) local t1, t2, L1, L2, L, d, i;

t1:=convert(m, base, b); L1:=nops(t1);

t2:=convert(n, base, b); L2:=nops(t2); L:=L1;

if L2<L1 then for i from 1 to L1-L2 do t2:=[op(t2), 0]; od;

elif L1<L2 then for i from 1 to L2-L1 do t1:=[op(t1), 0]; od; L:=L2;

fi;

d:=0;

for i from 1 to L do if t1[i]<>t2[i] then d:=d+1; fi; od;

d; end;

# Build lexicode with min distance D in base b, search up to M

# C = size of code found, tooc = 1 means too close to code

unprotect(D);

lexicode := proc(D, b, M) local cod, v, i, tooc, C;

cod:=[0]; C:=1;

# can we add v ?

for v from 0 to M do

   tooc:=-1;

   for i from 1 to C do

   if Hammdist(v, cod[i], b)<D then tooc:=1; break; fi;

                     od:

if tooc = -1 then C:=C+1; cod:=[op(cod), v]; fi;

od:

cod;

end;

CROSSREFS

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.

Sequence in context: A072434 A033285 A085109 * A074843 A175464 A326110

Adjacent sequences:  A345997 A345998 A345999 * A346001 A346002 A346003

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Jul 20 2021

STATUS

approved

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Last modified October 23 11:49 EDT 2021. Contains 348212 sequences. (Running on oeis4.)