A104628 Numbers having 5 1's in their base-phi representation.

11, 15, 22, 23, 24, 26, 30, 31, 32, 34, 35, 37, 41, 42, 43, 45, 46, 51, 52, 53, 55, 66, 83, 95, 112, 127, 128, 129, 131, 142, 171, 217, 247, 293, 326, 327, 328, 330, 341, 370, 446, 568, 645, 767, 847, 848, 849, 851, 862, 891, 967, 1166, 1487, 1687, 2008, 2211

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..300

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 46-state automaton accepting precisely 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]] == 5; Select[Range[2000], q] (* Amiram Eldar, Jan 20 2022 *)

Crossrefs

Cf. A005248, A104626, A104627.

Sequence in context: A213179 A211322 A087682 * A045564 A285271 A087142

Adjacent sequences: A104625 A104626 A104627 * A104629 A104630 A104631

Keyword

nonn,base

Author

Eric W. Weisstein, Mar 17 2005

Status

approved