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%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
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