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A178905 Numbers without 3 consecutive equal digits in any base b >= 2.

%I A178905 #15 Mar 28 2022 01:31:52
%S A178905 0,1,2,3,4,5,6,9,10,11,12,18,19,20,22,25,36,37,38,44,45,50,51,52,74,
%T A178905 75,76,77,89,90,100,101,102,105,109,147,150,153,154,165,166,173,178,
%U A178905 179,180,181,204,205,210,212,214,217,293,294,299,300,301,306,308,309,329
%N A178905 Numbers without 3 consecutive equal digits in any base b >= 2.
%H A178905 Michael S. Branicky, <a href="/A178905/b178905.txt">Table of n, a(n) for n = 1..10000</a>
%t A178905 Prepend[Cases[Range[329], n_ /; NoneTrue[Range[2, (Sqrt[4 n - 3] - 1)/2], MatchQ[IntegerDigits[n, #], {___, d_, d_, d_, ___}] &]], 0] (* _Vladimir Reshetnikov_, Mar 20 2022 *)
%o A178905 (Python)
%o A178905 from sympy.ntheory.digits import digits
%o A178905 def three_in_a_row(s):
%o A178905     return any(s[i] == s[i+1] == s[i+2] for i in range(len(s) - 2))
%o A178905 def ok(n):
%o A178905     if n < 7: return True
%o A178905     b = 2
%o A178905     d = digits(n, b)[1:]
%o A178905     while len(d) >= 3:
%o A178905         if three_in_a_row(d): return False
%o A178905         b += 1
%o A178905         d = digits(n, b)[1:]
%o A178905     return True
%o A178905 print([k for k in range(331) if ok(k)]) # _Michael S. Branicky_, Mar 27 2022
%Y A178905 Cf. A063037.
%K A178905 base,nonn
%O A178905 1,3
%A A178905 _Joonas Pohjonen_, Jun 22 2010