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A254123 Least number of terms needed to build n from Fibonacci numbers using + and *. 2
1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 3, 3, 1, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 1, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 3, 1, 2, 2, 2, 3, 2, 3, 3, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 1, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
a(n) = 1 iff n is a Fibonacci number (A000045).
a(n) = 2 iff n is in A254122.
a(A025282(n)) = n.
LINKS
EXAMPLE
a(40) = 2 because 40 = 5*8; 5 and 8 are Fibonacci numbers but 40 is not.
MAPLE
N:= 1000: # to get a(1) to a(N)
A:= Vector(N):
for i from 1 do
f:= combinat:-fibonacci(i);
if f > N then break fi;
A[f]:= 1
od:
for n from 1 to N do
if A[n] = 0 then
m:= floor(n/2);
r:= min(A[1..m] + A[[seq(n-i, i=1..m)]]);
for a in select(`<=`, numtheory:-divisors(n) minus {1}, floor(sqrt(n))) do
r:= min(r, A[a] + A[n/a])
od:
A[n]:= r;
fi
od:
seq(A[i], i=1..N);
CROSSREFS
Sequence in context: A352884 A102382 A024890 * A007895 A053260 A267135
KEYWORD
nonn
AUTHOR
Robert Israel, Jan 25 2015
STATUS
approved

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Last modified July 19 12:04 EDT 2024. Contains 374394 sequences. (Running on oeis4.)