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A349955 Numbers whose representation in any base b >= 2 is a cubefree word.

%I A349955 #19 Mar 28 2022 07:43:43
%S A349955 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 A349955 75,76,77,89,90,100,101,102,105,109,147,150,153,154,165,166,173,178,
%U A349955 179,180,181,204,205,210,214,217,293,294,300,301,306,308,309,329,330
%N A349955 Numbers whose representation in any base b >= 2 is a cubefree word.
%C A349955 A subsequence of A178905. A subsequence of A286262.
%H A349955 Michael S. Branicky, <a href="/A349955/b349955.txt">Table of n, a(n) for n = 1..10000</a>
%H A349955 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubefreeWord.html">Cubefree Word</a>.
%t A349955 Prepend[Cases[Range[330], n_ /; NoneTrue[Range[2, (Sqrt[4 n - 3] - 1)/2], MatchQ[IntegerDigits[n, #], {___, d__, d__, d__, ___}] &]], 0]
%o A349955 (Python)
%o A349955 from sympy.ntheory.digits import digits
%o A349955 def hascube(s):
%o A349955     for l in range(1, len(s)//3 + 1):
%o A349955       for i in range(len(s) - 3*l + 1):
%o A349955           if s[i:i+l] == s[i+l:i+2*l] == s[i+2*l:i+3*l]: return True
%o A349955     return False
%o A349955 def ok(n):
%o A349955     if n < 7: return True
%o A349955     b = 2
%o A349955     d = digits(n, b)[1:]
%o A349955     while len(d) >= 3:
%o A349955         if hascube(d):
%o A349955             return False
%o A349955         b += 1
%o A349955         d = digits(n, b)[1:]
%o A349955     return True
%o A349955 print([k for k in range(331) if ok(k)]) # _Michael S. Branicky_, Mar 27 2022
%Y A349955 Cf. A178905, A286262.
%K A349955 nonn,base
%O A349955 1,3
%A A349955 _Vladimir Reshetnikov_, Mar 20 2022