%I #2 Feb 11 2014 19:05:33
%S 2,3,5,7,8,9,11,13,14,15,18,21,22,23,24,29,34,35,36,37,39,47,55,56,57,
%T 58,60,63,76,89,90,91,92,94,97,102,123,144,145,146,147,149,152,157,
%U 165,199,233,234,235,236,238,241,246,254,267,322,377,378,379,380,382,385
%N Numbers with exactly one representation as the sum of two Fibonacci numbers.
%e 1000 has exactly one representation as the sum of Fibonacci numbers: 1000 = 13 + 987. Hence 1000 belongs to the sequence.
%t r = {}; f = Table[Fibonacci[n], {n, 1, 20}]; FibQ[n_] := MemberQ[f, n]; g[n_] := Module[{a, i}, a = {}; u = Floor[n/2]; For[i = 1, i <= u, i++, If[FibQ[i] && FibQ[n - i], a = Append[a, {n, i, n - i}]]]; a]; For[i = 1, i <= 10^3, i++, If[Length[g[i]] == 1, r = Append[r, i]]]; r
%K nonn
%O 1,1
%A _Joseph L. Pe_, Dec 12 2002