A254122 -id:A254122 - cp's OEIS frontend

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

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

Offset: 1

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

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

			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

Sean A. Irvine, Java program (github)

Cf. A000045, A254122, A254123.

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

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

A254123 Least number of terms needed to build n from Fibonacci numbers using + and *.

Original entry on oeis.org

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

Offset: 1

Robert Israel, Jan 25 2015

nonn

a(n) = 1 iff n is a Fibonacci number (A000045).
a(n) = 2 iff n is in A254122.
a(A025282(n)) = n.

			a(40) = 2 because 40 = 5*8; 5 and 8 are Fibonacci numbers but 40 is not.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000045, A025282, A254122.

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);

cp's OEIS Frontend

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

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