A343444 - OEIS

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

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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