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A173804
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a(n) = (5*10^n - 41)/9 for n > 0.
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4
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1, 51, 551, 5551, 55551, 555551, 5555551, 55555551, 555555551, 5555555551, 55555555551, 555555555551, 5555555555551, 55555555555551, 555555555555551, 5555555555555551, 55555555555555551, 555555555555555551
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OFFSET
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1,2
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COMMENTS
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Primes up to n=100 are 555555555551 and 5555555555551; the next prime term has 609 digits (see A056684).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..100
Index entries for linear recurrences with constant coefficients, signature (11,-10).
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FORMULA
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a(n) = 10*a(n-1) + 41 with a(0)=-4.
G.f.: x*(1+40*x)/((1-x)*(1-10*x)). - Vincenzo Librandi, Jul 05 2012
a(n) = 11*a(n-1) - 10*a(n-2). - Vincenzo Librandi, Jul 05 2012
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MATHEMATICA
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CoefficientList[Series[(1+40*x)/((1-x)*(1-10*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 05 2012 *)
Table[FromDigits[PadLeft[{1}, n, 5]], {n, 20}] (* or *) LinearRecurrence[ {11, -10}, {1, 51}, 20](* Harvey P. Dale, Dec 04 2021 *)
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PROG
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(MAGMA)[(5*10^n-41)/9: n in [1..20]]; // Vincenzo Librandi, Jul 05 2012
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CROSSREFS
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Cf. A056684 (numbers n such that (5*10^(n+1)-41)/9 is prime). - Klaus Brockhaus, Feb 28 2010
Sequence in context: A142994 A251932 A319542 * A166820 A269438 A269622
Adjacent sequences: A173801 A173802 A173803 * A173805 A173806 A173807
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Feb 25 2010
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STATUS
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approved
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