A104627 Numbers having 4 1's in their base-phi representation.

9, 10, 12, 13, 14, 16, 17, 20, 21, 25, 36, 49, 50, 54, 65, 94, 125, 126, 130, 141, 170, 246, 324, 325, 329, 340, 369, 445, 644, 845, 846, 850, 861, 890, 966, 1165, 1686, 2209, 2210, 2214, 2225, 2254, 2330, 2529, 3050, 4414

Offset: 1

Author

Eric W. Weisstein, Mar 17 2005

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..250
• Jeffrey Shallit, Proving Properties of phi-Representations with the Walnut Theorem-Prover, arXiv:2305.02672 [math.NT], 2023.
• Eric Weisstein's World of Mathematics, Phi Number System.

Crossrefs

Cf. A005248, A104626, A104628.

Programs

Mathematica

q[n_] := Plus @@ RealDigits[n, GoldenRatio, 2*Ceiling[ Log[GoldenRatio, n]] ][[1]] == 4; Select[Range[4500], q] (* Amiram Eldar, Jan 20 2022 *)

Formula

There is a 24-state automaton accepting exactly the Zeckendorf representation of members of this sequence. - Jeffrey Shallit, May 03 2023