A214977 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

See the conjecture at A214979.

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

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

Sequence in context: A018649 A341159 A374177 * A135676 A102701 A255770

Adjacent sequences: A214974 A214975 A214976 * A214978 A214979 A214980

KEYWORD

nonn

AUTHOR

Clark Kimberling, Oct 22 2012

STATUS

approved