A179242 Numbers that have two terms in their Zeckendorf representation.

4, 6, 7, 9, 10, 11, 14, 15, 16, 18, 22, 23, 24, 26, 29, 35, 36, 37, 39, 42, 47, 56, 57, 58, 60, 63, 68, 76, 90, 91, 92, 94, 97, 102, 110, 123, 145, 146, 147, 149, 152, 157, 165, 178, 199, 234, 235, 236, 238, 241, 246, 254, 267, 288, 322, 378, 379, 380, 382, 385, 390

Offset

1,1

Comments

A007895(a(n)) = 2. - Reinhard Zumkeller, Mar 10 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

4 = 1+3;
6 = 1+5;
7 = 2+5;
9 = 1+8;
10 = 2+8;

Maple

with(combinat): B := proc (n) local A, ct, m, j: A := proc (n) local i; for i while fibonacci(i) <= n do n-fibonacci(i) end do end proc: ct := 0: m := n: for j while 0 < A(m) do ct := ct+1: m := A(m) end do: ct+1 end proc: Q := {}: for i from fibonacci(5)-1 to 400 do if B(i) = 2 then Q := `union`(Q, {i}) else end if end do: Q;

Mathematica

f[n_] := (k = 1; ff = {}; While[(fi = Fibonacci[k]) <= n, AppendTo[ff, fi]; k++]; Drop[ff, 1]); z[n_] := If[n == 0, 0, r = n; s = {}; fr = f[n]; While[r > 0, lf = Last[fr]; If[lf <= r, r = r - lf; PrependTo[s, lf]]; fr = Drop[fr, -1]]; s]; Select[ Range[400], Length[z[#]] == 2 &] (* Jean-François Alcover, Sep 27 2011 *)
zeck = DigitCount[Select[Range[5000], BitAnd[#, 2*#] == 0&], 2, 1];
Position[zeck, 2] // Flatten (* Jean-François Alcover, Jan 25 2018 *)

Prog

(Haskell)
import Data.List (inits)
a179242 n = a179242_list !! (n-1)
a179242_list = concatMap h $ drop 3 $ inits $ drop 2 a000045_list where
   h is = reverse $ map (+ f) fs where
          (f:_:fs) = reverse is
-- Reinhard Zumkeller, Mar 10 2013

Crossrefs

Cf. A035517, A007895, A179243, A179244, A179245, A179246, A179247, A179248, A179249, A179250, A179251, A179252, A179253.

Cf. A000045.

Sequence in context: A010414 A254122 A095096 * A104425 A345447 A174258

Adjacent sequences: A179239 A179240 A179241 * A179243 A179244 A179245

Keyword

nonn

Author

Emeric Deutsch, Jul 05 2010

Status

approved