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Search: id:A010859
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| 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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If A=[A157659] 100*n.^2-n (99, 398, 897, ,.,); Y=[A010859] 20 (20, 20, 20,. ,.,); X=[A157955] 200*n-1 (199, 399, 599,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 199^2-99 *20^2=1; 399^2-398*20^2=1; 599^2-897*20^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009]
If A=[A158312] 400*n.^2+2*n (n>0, 402, 1604, 3606,.,); Y=[A010859] 20 (20, 20, 20 ,.,); X=[A158313] 400*n+1 (n>0, 401, 801, 1201, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 401^2-402*20^2=1; 801^2-1604*20^2=1; 1201^2-3606*20^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 16 2009]
If A=[A158316] 400*n.^2-2*n (n>0, 398, 1596, 3594,.,); Y=[A010859] 20 (20, 20, 20 ,.,); X=[A158317] 400*n-1 (n>0, 399, 799, 1199, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 399^2-398*20^2=1; 799^2-1596*20^2=1; 1199^2-3594*20^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 16 2009]
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LINKS
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Tanya Khovanova, Recursive Sequences
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CROSSREFS
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Cf. A157659, A157955 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009]
Cf. A158312, A158313 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 16 2009]
Cf. A158316, A158317 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 16 2009]
Sequence in context: A023462 A087708 A081245 this_sequence A040381 A022354 A165841
Adjacent sequences: A010856 A010857 A010858 this_sequence A010860 A010861 A010862
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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