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

Author

Peter Woodward, Jul 11 2021

Keywords

• nonn
• base

Examples

			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.
		

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.

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.

Programs

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

Extensions

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