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Search: id:A156842
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| 263, 46, 887, 2786, 5743, 9758, 14831, 20962, 28151, 36398, 45703, 56066, 67487, 79966, 93503, 108098, 123751, 140462, 158231, 177058, 196943, 217886, 239887, 262946, 287063, 312238, 338471, 365762, 394111, 423518, 453983, 485506, 518087
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OFFSET
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1,1
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COMMENT
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Arises in solving Pell equations of the form X^2 - A*Y^2 = 1.
Let n=[A156849] (156,373,685,902,...,) =n^2-2=0 mod (23^2). If A=[A156841] (46,263,1538,3871,.,) = 529*n^2-312*n+46 or A=[156842] (263,46,887,2787) =(529*n^2-746*n+263 , Y=23*n, or [A156845] (3588,15755,27922,...,) = 12167*n-8579, or Y=[A156846] (8579,20746,32913,...,) =12167*n-3588, and X=279841*n^2-165048*n+24335 [A156843] (24335,139128,813603,...,) or X=[A156844] =279841*n^2-394634*n+139128 (139128,24335,469224,1473795,...,) , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: For n=156, A=46, Y=3588, X=24335, 24335^2-46*3588^2=1 ; n=373, A=263, Y=8579, X=139128; 139128^2-263*8579^2=1; n=685, A=887, Y=15755, X=469224; 469224^2-887*15755^2=1; n=902, A=1538, Y=20746, X=813603; 813603^2-1538*20746^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
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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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EXAMPLE
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For n=0, a(0)=263; n=1, a(1)=46; n=2, a(2)=887; n=3, a(3)=2786
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CROSSREFS
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Cf. A156841
Cf. A156843, A156844, A156845, A156846, A156849 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A063364 A028536 A045179 this_sequence A052033 A105008 A142754
Adjacent sequences: A156839 A156840 A156841 this_sequence A156843 A156844 A156845
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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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