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A025282
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Smallest number requiring n Fibonacci numbers to build using + and *.
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3
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OFFSET
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1,2
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COMMENTS
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The n Fibonacci numbers need not be distinct. - Robert Israel, Jan 25 2015
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LINKS
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EXAMPLE
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a(12) = 1 + 3 + 8 but can't be represented using fewer than 3 Fibonacci numbers, and is the least number with this property. - Robert Israel, Jan 25 2015
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MAPLE
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N:= 50000: # to get a(n) where a(n) <= N
P:= Vector(N):
for i from 1 do
f:= combinat:-fibonacci(i);
if f > N then break fi;
P[f]:= 1
od:
A[1]:= 1:
rmax:= 1:
for n from 1 to N do
if P[n] = 0 then
m:= floor(n/2);
r:= min(P[1..m] + P[[seq(n-i, i=1..m)]]);
for a in select(`<=`, numtheory:-divisors(n) minus {1}, floor(sqrt(n))) do
r:= min(r, P[a] + P[n/a])
od:
P[n]:= r;
if r > rmax then
A[r]:= n;
rmax:= r;
fi
fi
od:
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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