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Search: id:A137879
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| A137879 |
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Numbers k such that k^2 is a 17-gonal number. |
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+0
4
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| 1, 133, 615, 64107, 296429, 30899441, 142878163, 14893466455, 68866978137, 7178619931869, 33193740583871, 3460079913694403, 15999314094447685, 1667751339780770377, 7711636199783200299, 803852685694417627311, 3716992648981408096433
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OFFSET
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1,2
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COMMENT
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Corresponding 17-gonal numbers equal k^2 are listed in A137878.
The 17-gonal numbers A051869(n) = n(15n - 13)/2 are perfect squares for indices n listed in A137880. Note that all such indices are also perfect squares of numbers listed in A137881.
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FORMULA
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a(n) = Sqrt[ A137878(n) ] = Sqrt[ A051869( A137880(n) ) ] = Sqrt[ A051869( A137881(n)^2 ) ].
For n>=5, a(n) = 482*a(n-2) - a(n-4). [Alekseyev]
a(2n) = (-60 + 17*sqrt(30))/120 * (11 + 2*sqrt(30))^(2n) + (-60 - 17*sqrt(30))/120 * (11 - 2*sqrt(30))^(2n). [Alekseyev]
a(2n+1) = (60 + 17*sqrt(30))/120 * (11 + 2*sqrt(30))^(2n) + (60 - 17*sqrt(30))/120 * (11 - 2*sqrt(30))^(2n). [Alekseyev]
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CROSSREFS
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Cf. A051869 (17-gonal numbers), A137878 (17-gonal numbers that are perfect squares), A137880, A137881.
Sequence in context: A064903 A070158 A055940 this_sequence A020237 A117565 A038491
Adjacent sequences: A137876 A137877 A137878 this_sequence A137880 A137881 A137882
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 19 2008
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EXTENSIONS
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Edited and extended by Max Alekseyev, Oct 19 2008
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