OFFSET
1,3
COMMENTS
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.
LINKS
Eric Weisstein's World of Mathematics, Cubefree Word.
Eric Weisstein's World of Mathematics, Zeckendorf Representation.
Wikipedia, Zeckendorf's theorem.
EXAMPLE
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.
MATHEMATICA
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]
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Vladimir Reshetnikov, Mar 19 2022
STATUS
approved