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A256657
Numbers for which the minimal alternating Fibonacci representation has negative trace.
4
4, 6, 7, 10, 11, 12, 16, 18, 19, 20, 25, 26, 29, 31, 32, 33, 38, 40, 41, 42, 46, 47, 50, 52, 53, 54, 59, 61, 62, 65, 66, 67, 68, 72, 74, 75, 76, 80, 81, 84, 86, 87, 88, 93, 95, 96, 99, 100, 101, 105, 107, 108, 109, 110, 114, 116, 117, 120, 121, 122, 123, 127
OFFSET
1,1
COMMENTS
See A256655 for definitions. This sequence and A256656 partition the positive integers.
LINKS
EXAMPLE
Let R(k) be the minimal alternating Fibonacci representation of k. The trace of R(k) is the last term.
R(1) = 1, trace = 1
R(2) = 2, trace = 2
R(3) = 3, trace = 3
R(4) = 5 - 1, trace = -1
R(5) = 5, trace = 5
R(6) = 6 - 2, trace = -2
MATHEMATICA
b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}];
h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]];
g = h[18]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]
t = Table[Last[r[n]], {n, 0, 1000}]; (* A256656 *)
Select[Range[200], Last[r[#]] > 0 &] (* A256656 *)
Select[Range[200], Last[r[#]] < 0 &] (* A256657 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 08 2015
STATUS
approved