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Search: id:A044812
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| A044812 |
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Numbers n such that string 9,9 occurs in the base 10 representation of n but not of n+1. |
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3
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| 99, 199, 299, 399, 499, 599, 699, 799, 899, 999, 1099, 1199, 1299, 1399, 1499, 1599, 1699, 1799, 1899, 1999, 2099, 2199, 2299, 2399, 2499, 2599, 2699, 2799, 2899, 2999, 3099, 3199, 3299, 3399, 3499, 3599, 3699, 3799, 3899
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If A=[A158129] 100*n.^2-2*n (n>0, 98, 396, 894,.,. ,.,); Y=[A010692] 10 (10, 10, 10,.,); X=[A044812] 100*n-1 (n>0, 99, 199, 299, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 99^2-98*10^2=1; 199^2-396*10^2=1; 299^2-894*10^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
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LINKS
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Tanya Khovanova, Non Recursions
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FORMULA
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a(n)=100*n-1 (n>0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
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EXAMPLE
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For n=1, a(1)=99; n=2, a(2)=199; n=3, a(3)=299 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
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CROSSREFS
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Cf. A158129, A010692 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
Adjacent sequences: A044809 A044810 A044811 this_sequence A044813 A044814 A044815
Sequence in context: A043526 A031500 A044431 this_sequence A125820 A008902 A008882
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KEYWORD
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nonn,base
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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