A007298 - OEIS

%I #30 Nov 16 2023 08:45:18

%S 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,

%T 50,52,53,54,55,68,76,81,84,86,87,88,89,110,123,131,136,139,141,142,

%U 143,144,178,199,212,220,225,228,230,231,232,233,288,322

%N Sums of consecutive Fibonacci numbers.

%C 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

%H T. D. Noe, <a href="/A007298/b007298.txt">Table of n, a(n) for n = 1..1000</a>

%F log a(n) >> sqrt(n). - _Charles R Greathouse IV_, Oct 06 2016

%p isA007298 := proc(n)

%p     local i,Fi,j,Fj ;

%p     for i from 0 do

%p         Fi := combinat[fibonacci](i) ;

%p         for j from i do

%p             Fj :=combinat[fibonacci](j) ;

%p             if Fj-Fi = n then

%p                 return true;

%p             elif Fj-Fi > n then

%p                 break;

%p             end if;

%p         end do:

%p         Fj :=combinat[fibonacci](i+1) ;

%p         if Fj-Fi > n then

%p             return false;

%p         end if;

%p     end do:

%p end proc:

%p for n from 0 to 100 do

%p     if isA007298(n) then

%p         printf("%d,",n) ;

%p     end if;

%p end do: # _R. J. Mathar_, May 25 2016

%t Union[Flatten[Table[Fibonacci[n]-Fibonacci[i], {n, 14}, {i, n}]]] (* _T. D. Noe_, Oct 17 2005 *)

%t 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]]];

%t Select[Range[0, 1000], isA007298] (* _Jean-François Alcover_, Nov 16 2023, after _R. J. Mathar_ *)

%o (PARI) A130233(n)=log(sqrt(5)*n+1.5)\log((1+sqrt(5))/2)

%o 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

%Y Cf. A000045, A050939.

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

%Y Cf. A219114 (numbers whose squares are here).

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Jan 02 2000