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%I #21 May 07 2016 00:33:45
%S 2,4,6,7,10,11,12,16,18,19,20,26,29,31,32,33,42,47,50,52,53,54,68,76,
%T 81,84,86,87,88,110,123,131,136,139,141,142,143,178,199,212,220,225,
%U 228,230,231,232,288,322,343,356,364,369,372,374,375,376,466,521,555,576
%N Sum of three or more consecutive Fibonacci numbers.
%C Except the first term that is 2, this sequence lists non-Fibonacci numbers (A001690) that are the difference of two Fibonacci numbers. So 2 is the only Fibonacci number in this sequence.
%C Since the sum of two consecutive Fibonacci numbers is obviously a Fibonacci number because of the definition of Fibonacci numbers, this sequence focuses on the sum of three or more consecutive Fibonacci numbers.
%e 4 is a term because Fibonacci(1) + Fibonacci(2) + Fibonacci(3) = 1 + 1 + 2 = 4.
%t mx=10^4; i=1; Union@ Reap[ While[(s = Plus @@ Fibonacci[i + {0,1,2}]) <= mx, j = ++i + 1; While[s <= mx, Sow@s; s += Fibonacci@ ++j]]][[2, 1]] (* _Giovanni Resta_, May 04 2016 *)
%Y Cf. A000045, A001690, A007298.
%K nonn
%O 1,1
%A _Altug Alkan_, May 04 2016
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