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A007298 Sums of consecutive Fibonacci numbers.

%I A007298 #30 Nov 16 2023 08:45:18
%S A007298 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 A007298 50,52,53,54,55,68,76,81,84,86,87,88,89,110,123,131,136,139,141,142,
%U A007298 143,144,178,199,212,220,225,228,230,231,232,233,288,322
%N A007298 Sums of consecutive Fibonacci numbers.
%C A007298 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 A007298 T. D. Noe, <a href="/A007298/b007298.txt">Table of n, a(n) for n = 1..1000</a>
%F A007298 log a(n) >> sqrt(n). - _Charles R Greathouse IV_, Oct 06 2016
%p A007298 isA007298 := proc(n)
%p A007298     local i,Fi,j,Fj ;
%p A007298     for i from 0 do
%p A007298         Fi := combinat[fibonacci](i) ;
%p A007298         for j from i do
%p A007298             Fj :=combinat[fibonacci](j) ;
%p A007298             if Fj-Fi = n then
%p A007298                 return true;
%p A007298             elif Fj-Fi > n then
%p A007298                 break;
%p A007298             end if;
%p A007298         end do:
%p A007298         Fj :=combinat[fibonacci](i+1) ;
%p A007298         if Fj-Fi > n then
%p A007298             return false;
%p A007298         end if;
%p A007298     end do:
%p A007298 end proc:
%p A007298 for n from 0 to 100 do
%p A007298     if isA007298(n) then
%p A007298         printf("%d,",n) ;
%p A007298     end if;
%p A007298 end do: # _R. J. Mathar_, May 25 2016
%t A007298 Union[Flatten[Table[Fibonacci[n]-Fibonacci[i], {n, 14}, {i, n}]]] (* _T. D. Noe_, Oct 17 2005 *)
%t A007298 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 A007298 Select[Range[0, 1000], isA007298] (* _Jean-François Alcover_, Nov 16 2023, after _R. J. Mathar_ *)
%o A007298 (PARI) A130233(n)=log(sqrt(5)*n+1.5)\log((1+sqrt(5))/2)
%o A007298 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 A007298 Cf. A000045, A050939.
%Y A007298 Cf. A113188 (primes that are the difference of two Fibonacci numbers).
%Y A007298 Cf. A219114 (numbers whose squares are here).
%K A007298 nonn,easy
%O A007298 1,3
%A A007298 _N. J. A. Sloane_, Jan 02 2000