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A007298
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Sums of consecutive Fibonacci numbers.
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12
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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
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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FORMULA
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MAPLE
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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;
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MATHEMATICA
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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]]];
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PROG
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(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
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CROSSREFS
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Cf. A113188 (primes that are the difference of two Fibonacci numbers).
Cf. A219114 (numbers whose squares are here).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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