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Search: id:A124130
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| A124130 |
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Numbers n such that L_n = a^2 + b^2, where L_n is the n-th Lucas number and a,b are integers. |
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+0
1
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| 1, 3, 6, 7, 13, 19, 30, 31, 37, 43, 49, 61, 67, 73, 78, 79, 91, 111, 127, 150, 163, 169, 183, 199
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Congruence considerations eliminate many indices, but the remaining numbers were factored. These have no prime factors of the form p=4m+3 dividing them to an odd power. Joint work with Kevin O'Bryant and Dennis Eichhorn.
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EXAMPLE
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a(5)=13 because the first five Lucas numbers that are the sum of two squares are L_1, L_3, L_6, L_7 and L_13=521=11^2+20^2.
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CROSSREFS
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Intersection of A000032 or A000204 = Lucas numbers and A001481.
Sequence in context: A033053 A107850 A051218 this_sequence A124132 A064291 A137473
Adjacent sequences: A124127 A124128 A124129 this_sequence A124131 A124132 A124133
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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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