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%I A111378 #14 Jun 04 2024 02:16:17
%S A111378 0,1,4,9,16,36,144,1600,14930496
%N A111378 Squares that are equal to the sum of two Fibonacci numbers.
%C A111378 Any further terms have more than 10,000 digits. - _Charles R Greathouse IV_, Sep 16 2015
%p A111378 Fibs:= {seq(combinat:-fibonacci(i),i=0..100)}:
%p A111378 sort(convert(select(issqr,{seq(seq(Fibs[i]+Fibs[j],j=1..i),i=1..100)}),list)); # _Robert Israel_, Jun 03 2024
%t A111378 Select[Union[Total/@Subsets[Fibonacci[Range[0,100]],{2}],Table[Fibonacci[n]*2,{n,0,100}]],IntegerQ[Sqrt[#]]&] (* _James C. McMahon_, Jun 03 2024 *)
%o A111378 (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
%Y A111378 Squares in A084176 (or A059389). Cf. A000045.
%K A111378 nonn
%O A111378 1,3
%A A111378 _Giovanni Teofilatto_, Nov 09 2005
%E A111378 1600 from _Jonathan Vos Post_, Nov 11 2005
%E A111378 14930496 from _N. J. A. Sloane_, Nov 11 2005

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