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Search: id:A156840
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| A156840 |
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Positive a(n) >1 such that a(n)^2 == 1 ( mod 900 ). |
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+0
6
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| 199, 251, 449, 451, 649, 701, 899, 901, 1099, 1151, 1349, 1351, 1549, 1601, 1799, 1801, 1999, 2051, 2249, 2251, 2449, 2501, 2699, 2701, 2899, 2951, 3149, 3151, 3349, 3401, 3599, 3601, 3799, 3851, 4049, 4051, 4249, 4301, 4499, 4501, 4699, 4751, 4949, 4951
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence serves in the following solutions of Pell equations [optionally
replace 900 by (A010869(n))^2 to visualize the Pell format of the equations]:
( a(4n+1) )^2 - A156810(n+1)*900 = 1, n>=0.
( a(4n+2) )^2 - A156812(n+1)*900 = 1, n>=0.
( a(4n+3) )^2 - A156813(n+1)*900 = 1, n>=0.
( a(4n+4) )^2 - A156814(n+1)*900 = 1, n>=0.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
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FORMULA
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a(n)=a(n-1)+a(n-4)-a(n-5). [R. J. Mathar, Aug 18 2009]
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EXAMPLE
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199^2-1==0 (mod 900). 251^2-1==0 (mod 900).
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CROSSREFS
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Cf. A156810, A156812, A156813, A156814, A010869 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A106628 A109561 A031930 this_sequence A142232 A166459 A142682
Adjacent sequences: A156837 A156838 A156839 this_sequence A156841 A156842 A156843
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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), Feb 17 2009
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EXTENSIONS
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Edited and a(11) corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 18 2009
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