A343444 Smallest nonnegative integer such that altering at most one of its digits cannot result in a previous term.

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 110, 123, 132, 145, 154, 167, 176, 189, 198, 202, 213, 220, 231, 246, 257, 264, 275, 303, 312, 321, 330, 347, 356, 365, 374, 404, 415, 426, 437, 440, 451, 462, 473, 505, 514, 527, 536, 541, 550, 563, 572, 606, 617, 624, 635, 642, 653, 660, 671, 707, 716, 725, 734, 743, 752

Offset: 1

Author

Bert Dobbelaere, Apr 15 2021

Keywords

• base
• easy
• nonn

Comments

Allowing prepending the integer representation with zeros; this means the Hamming distance between two digit strings representing different terms is at least 2.

Numbers whose bitwise XOR of digits is equal to zero. - Jeremias M. Gomes, Jul 25 2021

Links

• 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.
• Wikipedia, Hamming distance

Crossrefs

Cf. A001969, A075928, A333568, A346261.

Programs

Python

def ham(m, n):
  s, t = str(min(m, n)), str(max(m, n))
  s = '0'*(len(t)-len(s)) + s
  return sum(s[i] != t[i] for i in range(len(t)))
def aupton(terms):
  alst = [0]
  for n in range(2, terms+1):
    an = alst[-1] + 1
    while any(ham(an, alst[-i]) < 2 for i in range(1, len(alst)+1)): an += 1
    alst.append(an)
  return alst
print(aupton(66)) # Michael S. Branicky, Apr 15 2021