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A214977
Number of terms in Lucas representations of 1,2,...,n.
4
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
1,2
COMMENTS
See the conjecture at A214979.
LINKS
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 22 2012
STATUS
approved