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A177051
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A subsequence of the Fibonacci sequence such that a(n) is a quadratic residue mod a(n+1).
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0
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1, 2, 34, 55, 89, 233, 377, 1597, 17711, 28657, 121393, 317811, 1346269, 3524578, 5702887, 24157817, 39088169, 63245986, 433494437, 2971215073, 53316291173, 591286729879, 956722026041, 2504730781961, 4052739537881, 17167680177565, 308061521170129, 5527939700884757, 61305790721611591, 99194853094755497, 1779979416004714189
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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).
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MAPLE
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with(combinat, fibonacci):k:=1:pr0:=fibonacci(k):for n from k+1 to 100 do:pr:=fibonacci(n):if
quadres(pr0, pr)=1then pr0:=pr:printf(`%d, `, pr):else fi:od:
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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