A214974 - OEIS

%I #5 Dec 04 2016 19:46:30

%S 1,2,3,6,9,10,14,15,17,22,27,28,36,38,41,43,44,46,52,58,59,61,62,66,

%T 69,74,75,81,84,94,95,96,98,107,112,114,117,119,120,122,128,131,136,

%U 139,148,152,153,154,155,159,161,164,173,175,176,181,182,184,185

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

%H Clark Kimberling, <a href="/A214974/b214974.txt">Table of n, a(n) for n = 1..8000</a>

%e k...Lucas.....Zeckendorf....counter

%e 1...1.........1.............a(1)= 1

%e 2...2.........2.............a(2)= 2

%e 3...3.........3.............a(3)= 3

%e 4...4.........3+1

%e 5...4+1.......5

%e 6...4+2.......5+1...........a(4)= 6

%e 7...7.........5+2

%e 8...7+1.......8

%e 9...7+2.......8+1...........a(5)= 9

%t u = Reverse[Sort[Table[LucasL[n - 1], {n, 1, 50}]]];

%t u1 = Map[Length[Select[Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, #, u]][[2,1]], # > 0 &]] &, Range[1000]];

%t v = Reverse[Table[Fibonacci[n + 1], {n, 1, 50}]];

%t v1 = Map[Length[Select[Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, #, v]][[2,1]], # > 0 &]] &, Range[1000]];

%t s[n_] := If[u1[[n]] == v1[[n]], 1, 0];

%t s1 = Table[s[n], {n, 1, 200}];

%t f1 = Flatten[Position[s1, 1]] (* A214974 *)

%t s[n_] := If[u1[[n]] < v1[[n]], 1, 0];

%t s2 = Table[s[n], {n, 1, 200}];

%t f2 = Flatten[Position[s2, 1]] (* A214975 *)

%t s[n_] := If[u1[[n]] > v1[[n]], 1, 0];

%t s3 = Table[s[n], {n, 1, 200}];

%t f3 = Flatten[Position[s3, 1]] (* A214976 *)

%t (* _Peter J. C. Moses_ *)

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

%K nonn

%O 1,2

%A _Clark Kimberling_, Oct 20 2012