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Search: id:A157506
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| A157506 |
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a(n)=13122*n^2+324*n+1 (n>0) |
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+0
3
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| 13447, 53137, 119071, 211249, 329671, 474337, 645247, 842401, 1065799, 1315441, 1591327, 1893457, 2221831, 2576449, 2957311, 3364417, 3797767, 4257361, 4743199, 5255281, 5793607, 6358177, 6948991, 7566049, 8209351, 8878897
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OFFSET
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1,1
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COMMENT
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If A=[A031433] 81*n.^2+2*n (83,328,735,.,); Y=[A157505] 1458*n+18 (1476,2934,4392, 5850..,); X=[A157506] 13122*n^2+324*n+1 (13447,53137,119071,.,) ; , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: 13447^2-83*1476^2=1; 53137^2-328*2934^2=1; 119071^2-735*4392^2=1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=13122*n^2+324*n+1 (n>0)
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EXAMPLE
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For n=1, a(1)=13447; n=2, a(2)=53137; n=3, a(3)=119071
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CROSSREFS
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Cf. A031433, A157505
Sequence in context: A162423 A083598 A015300 this_sequence A035917 A115925 A029557
Adjacent sequences: A157503 A157504 A157505 this_sequence A157507 A157508 A157509
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 02 2009
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