A352335 Numbers whose representation in the Fibonacci base is a cubefree word.

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, 120, 134, 189, 194, 195, 218, 307, 315, 316, 353, 497, 511, 571, 572, 804, 805, 828, 925, 926, 1302, 1303, 2108

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

Table of n, a(n) for n=1..47.

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

Cf. A003714, A014417, A028445, A286262.

Sequence in context: A047518 A335031 A179834 * A361798 A242754 A120440

Adjacent sequences: A352332 A352333 A352334 * A352336 A352337 A352338

Keyword

nonn,base,fini,full

Author

Vladimir Reshetnikov, Mar 19 2022

Status

approved