Can any natural number be expressed in an increasing series (whole numbers, greater than 2 elements) in which the next element is the sum of the previous two elements? If so, what is the proof and how does one find some of these elements (such as Binets formula for the original Fibonacci sequence)?
2026-03-29 22:28:14.1774823294
Can any number be present in a Fibonacci-like sequence?
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The answer is trivially yes: Say you have the number $N$. Then take the sequence $$ A_0 = 1 \\ A_1 = N-1 \\ \forall k>1: A_k = A_{k-1}+A_{k-2} $$
Then $A_2 = N$.