A346261 Lexicographically earliest sequence of decimal words starting with 10 such that each term has Hamming distance at least 2 from all earlier terms.

10, 21, 32, 43, 54, 65, 76, 87, 98, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 201, 212, 220, 234, 245, 253, 267, 278, 286, 302, 313, 324, 330, 341, 356, 368, 375, 389, 397, 403, 414, 425, 431, 440, 452, 469, 496, 504, 515, 523, 536, 542, 550, 561, 579, 605, 616, 627, 638, 649, 651

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

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.

Example

a(1) = 10 by definition.
a(2) = 21 because '2' has not yet appeared in the tens place and '1' has not yet appeared in the ones place.

Prog

(Python)
def ham(m, n):
    s, t = str(min(m, n))[::-1], str(max(m, n))[::-1]
    return len(t) - len(s) + sum(s[i] != t[i] for i in range(len(s)))
def aupton(terms):
    alst = [10]
    for n in range(2, terms+1):
        an = alst[-1] + 1
        while any(ham(an, aprev) < 2 for aprev in alst[::-1]):  an += 1
        alst.append(an)
    return alst
print(aupton(60)) # Michael S. Branicky, Jul 22 2021

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.

Cf. A207063.

Sequence in context: A322828 A104341 A098954 * A061470 A095778 A065438

Adjacent sequences: A346258 A346259 A346260 * A346262 A346263 A346264

Keyword

nonn,base

Author

Peter Woodward, Jul 11 2021

Extensions

Edited and corrected by N. J. A. Sloane, Jul 20 2021

Status

approved