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
Keywords
Examples
4 = 1+3; 6 = 1+5; 7 = 2+5; 9 = 1+8; 10 = 2+8;
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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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 -
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 *) -
Python
from math import comb, isqrt from sympy import fibonacci def A179242(n): return fibonacci((m:=isqrt(n<<3)+1>>1)+3)+fibonacci(n+1-comb(m, 2)) # Chai Wah Wu, Apr 09 2025
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