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Search: id:A124134
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| A124134 |
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Numbers n such that F_n = a^2 + b^2, where F_n is the n-th Fibonacci number and a, b are integers. Note that all Fibonacci numbers with odd indices have this property. |
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+0
1
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| 1, 2, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 21, 23, 25, 26
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All odd numbers are in this sequence, since the Fibonacci number with index 2m+1 is the sum of the squares of the two Fibonacci numbers with indices m and m+1. Those with even indices ultimately depend on certain Lucas numbers being the sum of two squares. Joint work with Kevin O'Bryant and Dennis Eichhorn.
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EXAMPLE
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14 is in the sequence because F_14=377=11^2+16^2. 16 is not in the sequence because F_16=987 is congruent to 3 mod(4) and is thus known to not be such a sum.
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CROSSREFS
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Intersection of A000045 and A001481.
Adjacent sequences: A124131 A124132 A124133 this_sequence A124135 A124136 A124137
Sequence in context: A057196 A007071 A080637 this_sequence A085784 A085783 A143664
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KEYWORD
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nonn
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AUTHOR
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Melvin J. Knight (melknightdr(AT)verizon.net), Nov 30 2006
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