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

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

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..9.

Sean A. Irvine, Java program (github)

Example

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

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

Crossrefs

Cf. A000045, A254122, A254123.

Sequence in context: A149401 A149402 A045906 * A303392 A149403 A127866

Adjacent sequences: A025279 A025280 A025281 * A025283 A025284 A025285

Keyword

nonn,more

Author

David W. Wilson

Extensions

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

Status

approved