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Search: id:A157365
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| 51, 200, 447, 792, 1235, 1776, 2415, 3152, 3987, 4920, 5951, 7080, 8307, 9632, 11055, 12576, 14195, 15912, 17727, 19640, 21651, 23760, 25967, 28272, 30675, 33176, 35775, 38472, 41267, 44160, 47151, 50240, 53427, 56712, 60095, 63576, 67155
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OFFSET
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1,1
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COMMENT
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If A=[A157365] 49*n.^2+2*n (51,200,447,792,...,); Y=[A157366] 686*n+14 (700, 1386, 2072,2758,...,); X=[A157367] 4802*n^2+196*n+1 (4999,19601,43807,77617,...,) ; , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: 4999^2-51*700^2=1; 19601^2-200*1386^2=1; 43807^2-447*2072^2=1; 77617^2-792*2758^2=1.
If A=[A157365] 49*n.^2+2*n (n>0, 51, 200, 447,.,. ,.,); Y=[A010727] 7 (7,7,7,.,.,); X=[A158066] 49*n+1 (n>0, 50, 99, 148, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 50^2-51*7^2=1; 99^2-200*7^2=1; 148^2-447*7^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 12 2009]
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 12 2009]
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FORMULA
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a(n)=49*n^2+2*n (n>0)
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EXAMPLE
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For n=1, a(1)=51; n=2, a(2)=200; n=3, a(3)=447;
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CROSSREFS
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Cf. A157366, A157367
Cf. A158066, A010727 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 12 2009]
Sequence in context: A008883 A069762 A031431 this_sequence A157916 A007264 A158640
Adjacent sequences: A157362 A157363 A157364 this_sequence A157366 A157367 A157368
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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 28 2009
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