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Search: id:A156845
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| A156845 |
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a(n)=12167*n-8579 (n>0) |
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+0
7
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| 3588, 15755, 27922, 40089, 52256, 64423, 76590, 88757, 100924, 113091, 125258, 137425, 149592, 161759, 173926, 186093, 198260, 210427, 222594, 234761, 246928, 259095, 271262, 283429, 295596, 307763, 319930, 332097, 344264, 356431, 368598
(list; graph; listen)
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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=1, a(1)=3588; n=2, a(2)=15755; n=3, a(3)=27922
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CROSSREFS
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Cf. A156846
Cf. A156849, A156844, A156843, A156842, A156841 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A004932 A004952 A004972 this_sequence A157857 A141781 A096472
Adjacent sequences: A156842 A156843 A156844 this_sequence A156846 A156847 A156848
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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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