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

Author

N. J. A. Sloane, Jul 20 2021

Keywords

• nonn
• base

Comments

This is the distance 4 lexicode over the decimal alphabet.

Links

• 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.

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.

Programs

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 L2t2[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)