A214977 Number of terms in Lucas representations of 1,2,...,n.

1, 2, 3, 4, 6, 8, 9, 11, 13, 15, 16, 18, 20, 22, 24, 27, 30, 31, 33, 35, 37, 39, 42, 45, 47, 50, 53, 56, 57, 59, 61, 63, 65, 68, 71, 73, 76, 79, 82, 84, 87, 90, 93, 96, 100, 104, 105, 107, 109, 111, 113, 116, 119, 121, 124, 127, 130, 132, 135, 138, 141, 144

Offset: 1

Author

Clark Kimberling, Oct 22 2012

Keywords

• nonn

Comments

See the conjecture at A214979.

Examples

			n..Lucas(n)..# terms...A214977(n)
1..1.........1.........1
2..2.........1.........2
3..3.........1.........3
4..4.........1.........4
5..4+1.......2.........6
6..4+2.......2.........8
7..7.........1.........9
8..7+1.......2.........11
9..7+2.......2.........13
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A214978, A214979, A214980, A214981, A000032.

Programs

Mathematica

z = 200; s = Reverse[Sort[Table[LucasL[n - 1], {n, 1, 70}]]]; t1 = Map[Length[Select[Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, #, s]][[2,1]], # > 0 &]] &, Range[z]]; u[n_] := Sum[t1[[k]], {k, 1, n}]; u1 = Table[u[n], {n, 1, z}]
(* Peter J. C. Moses, Oct 18 2012 *)