A025282 Smallest number requiring n Fibonacci numbers to build using + and *.

1, 4, 12, 51, 373, 7724, 370555, 27284157, 2075178956

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• more

Comments

The n Fibonacci numbers need not be distinct. - Robert Israel, Jan 25 2015

a(10) > 4427000000. - Sean A. Irvine, Aug 23 2019

Examples

			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
		

Links

• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A000045, A254122, A254123.

Programs

Maple

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:
seq(A[i], i=1..rmax); # Robert Israel, Jan 25 2015

Extensions

a(7)-a(9) from Sean A. Irvine, Aug 23 2019