cp's OEIS Frontend

A256657 Numbers for which the minimal alternating Fibonacci representation has negative trace.

%I A256657 #4 Apr 09 2015 07:58:36
%S A256657 4,6,7,10,11,12,16,18,19,20,25,26,29,31,32,33,38,40,41,42,46,47,50,52,
%T A256657 53,54,59,61,62,65,66,67,68,72,74,75,76,80,81,84,86,87,88,93,95,96,99,
%U A256657 100,101,105,107,108,109,110,114,116,117,120,121,122,123,127
%N A256657 Numbers for which the minimal alternating Fibonacci representation has negative trace.
%C A256657 See A256655 for definitions.  This sequence and A256656 partition the positive integers.
%H A256657 Clark Kimberling, <a href="/A256657/b256657.txt">Table of n, a(n) for n = 1..1000</a>
%e A256657 Let R(k) be the minimal alternating Fibonacci representation of k.  The trace of R(k) is the last term.
%e A256657 R(1) = 1, trace = 1
%e A256657 R(2) = 2, trace = 2
%e A256657 R(3) = 3, trace = 3
%e A256657 R(4) = 5 - 1, trace = -1
%e A256657 R(5) = 5, trace = 5
%e A256657 R(6) = 6 - 2, trace = -2
%t A256657 b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
%t A256657 h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
%t A256657 g = h[18];  r[0] = {0};
%t A256657 r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]
%t A256657 t = Table[Last[r[n]], {n, 0, 1000}];  (* A256656 *)
%t A256657 Select[Range[200], Last[r[#]] > 0 &]  (* A256656 *)
%t A256657 Select[Range[200], Last[r[#]] < 0 &]  (* A256657 *)
%Y A256657 Cf. A000045, A256655, A256656.
%K A256657 nonn,easy
%O A256657 1,1
%A A256657 _Clark Kimberling_, Apr 08 2015