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A086695
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a(n) = 100^n - 10^n - 1.
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1
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89, 9899, 998999, 99989999, 9999899999, 999998999999, 99999989999999, 9999999899999999, 999999998999999999, 99999999989999999999, 9999999999899999999999, 999999999998999999999999, 99999999999989999999999999, 9999999999999899999999999999
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OFFSET
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1,1
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COMMENTS
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Digits of the inverses of these numbers give the Fibonacci numbers. More precisely, the digits of 1/(10^(2*n)-10^n-1) give the Fibonacci numbers up to 10^n.
More generally, if x_1, x_2, x_n=x_(n-1)-x_(n-2) is any Lucas sequence, then the digits of the numbers (x_1*10^n-(x_1-x_2))/(10^(2*n)-10^n-1) give the x_n up to 10^n.
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LINKS
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FORMULA
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a(n) = 10^(2*n) - 10^n - 1.
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MATHEMATICA
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Table[100^n-10^n-1, {n, 20}] (* or *) LinearRecurrence[{111, -1110, 1000}, {89, 9899, 998999}, 20] (* Harvey P. Dale, Nov 16 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Maurice Mischler (maurice.mischler(AT)ima.unil.ch), Sep 12 2003
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EXTENSIONS
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STATUS
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approved
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