cp's OEIS Frontend

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

%I A343444 #26 Aug 08 2021 02:02:49
%S A343444 0,11,22,33,44,55,66,77,88,99,101,110,123,132,145,154,167,176,189,198,
%T A343444 202,213,220,231,246,257,264,275,303,312,321,330,347,356,365,374,404,
%U A343444 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
%N A343444 Smallest nonnegative integer such that altering at most one of its digits cannot result in a previous term.
%C A343444 Allowing prepending the integer representation with zeros; this means the Hamming distance between two digit strings representing different terms is at least 2.
%C A343444 Numbers whose bitwise XOR of digits is equal to zero. - _Jeremias M. Gomes_, Jul 25 2021
%H A343444 J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1109/TIT.1986.1057187">Lexicographic codes: error-correcting codes from game theory</a>, IEEE Transactions on Information Theory, 32:337-348, 1986.
%H A343444 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamming_distance">Hamming distance</a>
%o A343444 (Python)
%o A343444 def ham(m, n):
%o A343444   s, t = str(min(m, n)), str(max(m, n))
%o A343444   s = '0'*(len(t)-len(s)) + s
%o A343444   return sum(s[i] != t[i] for i in range(len(t)))
%o A343444 def aupton(terms):
%o A343444   alst = [0]
%o A343444   for n in range(2, terms+1):
%o A343444     an = alst[-1] + 1
%o A343444     while any(ham(an, alst[-i]) < 2 for i in range(1, len(alst)+1)): an += 1
%o A343444     alst.append(an)
%o A343444   return alst
%o A343444 print(aupton(66)) # _Michael S. Branicky_, Apr 15 2021
%Y A343444 Cf. A001969, A075928, A333568, A346261.
%K A343444 base,easy,nonn
%O A343444 1,2
%A A343444 _Bert Dobbelaere_, Apr 15 2021