OFFSET
1,1
COMMENTS
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.
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.
EXAMPLE
4 is a term because Fibonacci(1) + Fibonacci(2) + Fibonacci(3) = 1 + 1 + 2 = 4.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, May 04 2016
STATUS
approved