A272631 Sum of three or more consecutive Fibonacci numbers.

2, 4, 6, 7, 10, 11, 12, 16, 18, 19, 20, 26, 29, 31, 32, 33, 42, 47, 50, 52, 53, 54, 68, 76, 81, 84, 86, 87, 88, 110, 123, 131, 136, 139, 141, 142, 143, 178, 199, 212, 220, 225, 228, 230, 231, 232, 288, 322, 343, 356, 364, 369, 372, 374, 375, 376, 466, 521, 555, 576

Offset: 1

Author

Altug Alkan, May 04 2016

Keywords

• nonn

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.

Examples

			4 is a term because Fibonacci(1) + Fibonacci(2) + Fibonacci(3) = 1 + 1 + 2 = 4.
		

Crossrefs

Cf. A000045, A001690, A007298.

Programs

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 *)