A111458 Numbers that cannot be represented as the sum of at most three Fibonacci numbers (with repetitions allowed).

33, 46, 51, 53, 54, 67, 72, 74, 75, 80, 82, 83, 85, 86, 87, 88, 101, 106, 108, 109, 114, 116, 117, 119, 120, 121, 122, 127, 129, 130, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 156, 161, 163, 164, 169, 171, 172

Offset: 1

Author

Stefan Steinerberger, Nov 15 2005

Keywords

• nonn

Examples

			33 is neither a Fibonacci number nor can be written as the sum of two or three Fibonacci numbers.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A000119, A179244, A135709.

Programs

Maple

isA111458 := proc(n) # returns true if n is in the sequence
    local xi,yi,x,y,z ;
    for xi from 0 do
        x := A000045(xi) ;
        if 3*x > n then
            return true;
        end if;
        for yi from xi do
            y := A000045(yi) ;
            if x+2*y > n then
                break;
            else
                z := n-x-y ;
                if isA000045(z) then # see isFib in A000045
                    return false;
                end if;
            end if;
        end do:
    end do:
end proc:
A111458 := proc(n)
    option remember;
    local a;
    if n = 0 then
        -1;
    else
        for a from procname(n-1)+1 do
            if isA111458(a) then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Sep 09 2015

Mathematica

FibQ[n_] := IntegerQ[Sqrt[5n^2+4]] || IntegerQ[Sqrt[5n^2-4]];
P[n_] := IntegerPartitions[n, 3, Select[Range[n], FibQ]];
Select[Range[1000], P[#] == {}&] (* Jean-François Alcover, Jul 20 2023 *)