_{1}=1, F

_{2}=2, for n=2,3,... F

_{n+1}= F

_{n}+ F

_{n-1}. The (n+1)-st number is the sum of n-th and (n-1)-th number in the sequence.

*Fibonacci numbers have the property that: the sum of the first n numbers of a sequence is contained in the sequence.*Do you know of others?

Actually the sequence GF

_{1}+F_{2}+F_{3}+...+F_{n}= F_{n+2}-1

_{1}=1, G

_{2}=2,for n=2,3,... G

_{n+1}= G

_{n}+ ... + G

_{2}+ G

_{1}trivially staifies that property. So, Fibonacci sequence is not unique in the above sense. Can you think of a sequence {H

_{k}} such that

On a tangent: Kolmogorov information complexity speaks of representations that can compress information effectively. Not only does the following set of characters "FH

_{1}+H_{2}+H_{3}+...+H_{n}= H_{n+3}- c? for some constant c.

_{1}=1, F

_{2}=2 F

_{n+1}= F

_{n}+ F

_{n-1}" contain the entire Fibonacci sequence, but also the sum of its first n elements.

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