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

1,1

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.

Links

Table of n, a(n) for n=1..60.

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

Cf. A000045, A001690, A007298.

Sequence in context: A325539 A002158 A319829 * A347694 A274431 A236477

Adjacent sequences: A272628 A272629 A272630 * A272632 A272633 A272634

Keyword

nonn

Author

Altug Alkan, May 04 2016

Status

approved