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A179242 Numbers that have two terms in their Zeckendorf representation.

%I A179242 #23 Apr 09 2025 14:13:32
%S A179242 4,6,7,9,10,11,14,15,16,18,22,23,24,26,29,35,36,37,39,42,47,56,57,58,
%T A179242 60,63,68,76,90,91,92,94,97,102,110,123,145,146,147,149,152,157,165,
%U A179242 178,199,234,235,236,238,241,246,254,267,288,322,378,379,380,382,385,390
%N A179242 Numbers that have two terms in their Zeckendorf representation.
%C A179242 A007895(a(n)) = 2. - _Reinhard Zumkeller_, Mar 10 2013
%H A179242 Reinhard Zumkeller, <a href="/A179242/b179242.txt">Table of n, a(n) for n = 1..10000</a>
%e A179242 4 = 1+3;
%e A179242 6 = 1+5;
%e A179242 7 = 2+5;
%e A179242 9 = 1+8;
%e A179242 10 = 2+8;
%p A179242 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;
%t A179242 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 *)
%t A179242 zeck = DigitCount[Select[Range[5000], BitAnd[#, 2*#] == 0&], 2, 1];
%t A179242 Position[zeck, 2] // Flatten (* _Jean-François Alcover_, Jan 25 2018 *)
%o A179242 (Haskell)
%o A179242 import Data.List (inits)
%o A179242 a179242 n = a179242_list !! (n-1)
%o A179242 a179242_list = concatMap h $ drop 3 $ inits $ drop 2 a000045_list where
%o A179242    h is = reverse $ map (+ f) fs where
%o A179242           (f:_:fs) = reverse is
%o A179242 -- _Reinhard Zumkeller_, Mar 10 2013
%o A179242 (Python)
%o A179242 from math import comb, isqrt
%o A179242 from sympy import fibonacci
%o A179242 def A179242(n): return fibonacci((m:=isqrt(n<<3)+1>>1)+3)+fibonacci(n+1-comb(m, 2)) # _Chai Wah Wu_, Apr 09 2025
%Y A179242 Cf. A035517, A007895, A179243, A179244, A179245, A179246, A179247, A179248, A179249, A179250, A179251, A179252, A179253.
%Y A179242 Cf. A000045.
%K A179242 nonn
%O A179242 1,1
%A A179242 _Emeric Deutsch_, Jul 05 2010