This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352335 #11 Mar 21 2022 11:55:49
%S A352335 0,1,2,3,4,6,7,10,11,12,16,17,19,27,28,31,44,45,50,51,72,74,82,83,117,
%T A352335 120,134,189,194,195,218,307,315,316,353,497,511,571,572,804,805,828,
%U A352335 925,926,1302,1303,2108
%N A352335 Numbers whose representation in the Fibonacci base is a cubefree word.
%C A352335 This is a finite sequence with 47 terms. The largest term is 2108, whose representation in the Fibonacci base is 1001001010010100, because 2108 = 1597 + 377 + 89 + 34 + 8 + 3.
%H A352335 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubefreeWord.html">Cubefree Word</a>.
%H A352335 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ZeckendorfRepresentation.html">Zeckendorf Representation</a>.
%H A352335 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zeckendorf%27s_theorem">Zeckendorf's theorem</a>.
%e A352335 17 can be expressed as a sum of distinct, non-consecutive Fibonacci numbers 13 + 3 + 1, so the representation of 17 in the Fibonacci base is 100101, which is a cubefree word, so 17 is in this sequence.
%t A352335 Cases[NestList[Function[n, {n[[1]] + 1, NestWhile[# + 1 &, n[[2]] + 1, BitAnd[#, 2 #] > 0 &]}], {0, 0}, 2108], {k_, z_} /; !MatchQ[IntegerDigits[z, 2], {___, w__, w__, w__, ___}] :> k]
%Y A352335 Cf. A003714, A014417, A028445, A286262.
%K A352335 nonn,base,fini,full
%O A352335 1,3
%A A352335 _Vladimir Reshetnikov_, Mar 19 2022