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

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

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