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