Problem 755

[haroldgparker]

Sometimes on Project Euler the term "sum" is construed as to necessitate at least two terms. I am wondering if sum has that meaning in the case of Problem 755 (View Problem). For instance, consider S(1). On the one hand, we know f(0) = 1, so S(1) >= 1. However, if we consider the lone Fibonacci term "1" an acceptable sum, then S(1) = 2.

So that's my question: does S(1) = 1 or 2? And by extension, can lone Fibonacci terms form sums? E.g., does f(13) count "13" as one of the sums?

[RobertStanforth]

So that's my question: does S(1) = 1 or 2? And by extension, can lone Fibonacci terms form sums? E.g., does f(13) count "13" as one of the sums?

Yes, $13$ counts towards $f(13)$: a sum is permitted to have a single term.
$f(1)=1$ because the single term $1$ qualifies as a sum.
$f(0)=1$ was chosen as the convention because 0 can be considered to be the sum of zero terms.
Hence $S(1)=2$.

[haroldgparker]

Thanks -- that makes things considerably simpler!