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

1,1

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.

Formula

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

Mathematica

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

Crossrefs

Cf. A005248, A104626, A104628.

Sequence in context: A136835 A031166 A202706 * A188057 A119956 A059102

Adjacent sequences: A104624 A104625 A104626 * A104628 A104629 A104630

Keyword

nonn,base

Author

Eric W. Weisstein, Mar 17 2005

Status

approved