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Search: id:A106257
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| A106257 |
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Numbers k such that k^2 = 12*n^2 + 13. |
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+0
2
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| 5, 11, 59, 149, 821, 2075, 11435, 28901, 159269, 402539, 2218331, 5606645, 30897365, 78090491, 430344779, 1087660229, 5993929541, 15149152715, 83484668795, 211000477781, 1162791433589, 2938857536219, 16195595401451
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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k(1)=5, k(2)=11, k(3)=14*k(1)-k(2), k(4)=14*k(2)-k(1) then k(n)=14*k(n-2)-k(n-4).
G.f.: (-11*x^3 - 5*x^2 + 149*x + 59)/(x^4 - 14*x^2 + 1).
a(2n) = (9*A001570(n)+A001570(n+1))/2, a(2n+1) = 5*A001570(n)-6*A007655(n).
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EXAMPLE
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5^2=12*1^2+13
11^2=12*3^2+13
59^2=12*17^2+13
149^2=12*43^2+13
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CROSSREFS
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Cf. A106256.
Adjacent sequences: A106254 A106255 A106256 this_sequence A106258 A106259 A106260
Sequence in context: A091798 A070198 A121934 this_sequence A104358 A104359 A104357
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KEYWORD
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nonn
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AUTHOR
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Pierre CAMI (pierrecami(AT)tele2.fr), Apr 28 2005
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EXTENSIONS
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Edited by Ralf Stephan, Jun 1 2007
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