A214974 Numbers k for which A116543(k) = A007895(k); i.e., the Lucas and Zeckendorf representations of k have the same length.

1, 2, 3, 6, 9, 10, 14, 15, 17, 22, 27, 28, 36, 38, 41, 43, 44, 46, 52, 58, 59, 61, 62, 66, 69, 74, 75, 81, 84, 94, 95, 96, 98, 107, 112, 114, 117, 119, 120, 122, 128, 131, 136, 139, 148, 152, 153, 154, 155, 159, 161, 164, 173, 175, 176, 181, 182, 184, 185

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..8000

Example

k...Lucas.....Zeckendorf....counter
1...1.........1.............a(1)= 1
2...2.........2.............a(2)= 2
3...3.........3.............a(3)= 3
4...4.........3+1
5...4+1.......5
6...4+2.......5+1...........a(4)= 6
7...7.........5+2
8...7+1.......8
9...7+2.......8+1...........a(5)= 9

Mathematica

u = Reverse[Sort[Table[LucasL[n - 1], {n, 1, 50}]]];
u1 = Map[Length[Select[Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, #, u]][[2, 1]], # > 0 &]] &, Range[1000]];
v = Reverse[Table[Fibonacci[n + 1], {n, 1, 50}]];
v1 = Map[Length[Select[Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, #, v]][[2, 1]], # > 0 &]] &, Range[1000]];
s[n_] := If[u1[[n]] == v1[[n]], 1, 0];
s1 = Table[s[n], {n, 1, 200}];
f1 = Flatten[Position[s1, 1]] (* A214974 *)
s[n_] := If[u1[[n]] < v1[[n]], 1, 0];
s2 = Table[s[n], {n, 1, 200}];
f2 = Flatten[Position[s2, 1]] (* A214975 *)
s[n_] := If[u1[[n]] > v1[[n]], 1, 0];
s3 = Table[s[n], {n, 1, 200}];
f3 = Flatten[Position[s3, 1]] (* A214976 *)
(* Peter J. C. Moses *)

Crossrefs

Cf. A116543, A007895, A214975, A214976, A214973.

Sequence in context: A047284 A268692 A089160 * A286434 A288930 A045588

Adjacent sequences: A214971 A214972 A214973 * A214975 A214976 A214977

Keyword

nonn

Author

Clark Kimberling, Oct 20 2012

Status

approved