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

Author

Vladimir Reshetnikov, Mar 19 2022

Keywords

• nonn
• base
• fini
• full

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.

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Cubefree Word.
• Eric Weisstein's World of Mathematics, Zeckendorf Representation.
• Wikipedia, Zeckendorf's theorem.

Crossrefs

Cf. A003714, A014417, A028445, A286262.

Programs

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]