A111378 - OEIS

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A111378

Squares that are equal to the sum of two Fibonacci numbers.

0, 1, 4, 9, 16, 36, 144, 1600, 14930496

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Any further terms have more than 10,000 digits. - Charles R Greathouse IV, Sep 16 2015

LINKS

Table of n, a(n) for n=1..9.

MAPLE

Fibs:= {seq(combinat:-fibonacci(i), i=0..100)}:

sort(convert(select(issqr, {seq(seq(Fibs[i]+Fibs[j], j=1..i), i=1..100)}), list)); # Robert Israel, Jun 03 2024

MATHEMATICA

Select[Union[Total/@Subsets[Fibonacci[Range[0, 100]], {2}], Table[Fibonacci[n]*2, {n, 0, 100}]], IntegerQ[Sqrt[#]]&] (* James C. McMahon, Jun 03 2024 *)

PROG

(PARI) list(lim)=my(F=List(), v=List([0, 1]), n=1, t); while((t=fibonacci(n++))<=lim, listput(F, t)); F=Vec(F); for(i=1, #F, for(j=i, #F, if(issquare(t=F[i]+F[j]), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Sep 16 2015

CROSSREFS

Squares in A084176 (or A059389). Cf. A000045.

Sequence in context: A363657 A231180 A250029 * A106313 A219355 A291216

Adjacent sequences: A111375 A111376 A111377 * A111379 A111380 A111381

KEYWORD

nonn

AUTHOR

Giovanni Teofilatto, Nov 09 2005

EXTENSIONS

1600 from Jonathan Vos Post, Nov 11 2005

14930496 from N. J. A. Sloane, Nov 11 2005

STATUS

approved