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%I
%S 1,2,34,55,89,233,377,1597,17711,28657,121393,317811,1346269,3524578,
%T 5702887,24157817,39088169,63245986,433494437,2971215073,53316291173,
%U 591286729879,956722026041,2504730781961,4052739537881,17167680177565,308061521170129,5527939700884757,61305790721611591,99194853094755497,1779979416004714189
%N A subsequence of the Fibonacci sequence such that a(n) is a quadratic residue mod a(n+1).
%e 2, 34 and 55 are in the sequence because L(2/34) = L(34/55) = 1 where L(a/b) is the Legendre symbol of a and b, which is defined to be 1 if a is a quadratic residue (mod b) and -1 if a is a quadratic non-residue (mod b).
%p with(combinat, fibonacci):k:=1:pr0:=fibonacci(k):for n from k+1 to 100 do:pr:=fibonacci(n):if
%p quadres(pr0,pr)=1then pr0:=pr:printf(`%d, `,pr):else fi:od:
%o (PARI) print1(k=1); for(n=3,100,t=fibonacci(n); if(issquare(Mod(k,t)), print1(", "k=t))) \\ _Charles R Greathouse IV_, Jan 09 2013
%Y Cf. A034794, A000045.
%K nonn
%O 1,2
%A _Michel Lagneau_, Dec 09 2010
%E Definition corrected by _Michel Lagneau_
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