A007298 Sums of consecutive Fibonacci numbers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 16, 18, 19, 20, 21, 26, 29, 31, 32, 33, 34, 42, 47, 50, 52, 53, 54, 55, 68, 76, 81, 84, 86, 87, 88, 89, 110, 123, 131, 136, 139, 141, 142, 143, 144, 178, 199, 212, 220, 225, 228, 230, 231, 232, 233, 288, 322

Offset: 1

Author

N. J. A. Sloane, Jan 02 2000

Keywords

• nonn
• easy

Comments

Also the differences between two Fibonacci numbers, because the difference F(i+2) - F(j+1) equals the sum F(j) + ... + F(i). - T. D. Noe, Oct 17 2005; corrected by Patrick Capelle, Mar 01 2008

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A050939.

Cf. A113188 (primes that are the difference of two Fibonacci numbers).

Cf. A219114 (numbers whose squares are here).

Programs

Maple

isA007298 := proc(n)
    local i,Fi,j,Fj ;
    for i from 0 do
        Fi := combinat[fibonacci](i) ;
        for j from i do
            Fj :=combinat[fibonacci](j) ;
            if Fj-Fi = n then
                return true;
            elif Fj-Fi > n then
                break;
            end if;
        end do:
        Fj :=combinat[fibonacci](i+1) ;
        if Fj-Fi > n then
            return false;
        end if;
    end do:
end proc:
for n from 0 to 100 do
    if isA007298(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, May 25 2016

Mathematica

Union[Flatten[Table[Fibonacci[n]-Fibonacci[i], {n, 14}, {i, n}]]] (* T. D. Noe, Oct 17 2005 *)
isA007298[n_] := Module[{i, Fi, j, Fj}, For[i = 0, True, i++, Fi = Fibonacci[i]; For[j = i, True, j++, Fj = Fibonacci[j]; Which[Fj - Fi == n, Return@True, Fj - Fi > n, Break[]]]; Fj := Fibonacci[i + 1]; If[Fj - Fi > n, Return@False]]];
Select[Range[0, 1000], isA007298] (* Jean-François Alcover, Nov 16 2023, after R. J. Mathar *)

PARI

A130233(n)=log(sqrt(5)*n+1.5)\log((1+sqrt(5))/2)
list(lim)=my(v=List([0]),F=vector(A130233(lim),i,fibonacci(i)),s,t); for(i=1,#F, s=0; forstep(j=i,1,-1, s+=F[j]; if(s>lim, break); listput(v,s))); Set(v) \\ Charles R Greathouse IV, Oct 06 2016

Formula

log a(n) >> sqrt(n). - Charles R Greathouse IV, Oct 06 2016