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A007298 Sums of consecutive Fibonacci numbers. 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
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
FORMULA
log a(n) >> sqrt(n). - Charles R Greathouse IV, Oct 06 2016
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 *)
PROG
(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
CROSSREFS
Cf. A113188 (primes that are the difference of two Fibonacci numbers).
Cf. A219114 (numbers whose squares are here).
Sequence in context: A242455 A339879 A274374 * A190856 A127033 A028826
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 02 2000
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)