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

1,2

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

Table of n, a(n) for n=1..66.

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

Prog

(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

Crossrefs

Cf. A001969, A075928, A333568, A346261.

Sequence in context: A065571 A064544 A083967 * A193772 A178359 A108203

Adjacent sequences: A343441 A343442 A343443 * A343445 A343446 A343447

Keyword

base,easy,nonn

Author

Bert Dobbelaere, Apr 15 2021

Status

approved