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A173804
a(n) = (5*10^n - 41)/9 for n > 0.
4
1, 51, 551, 5551, 55551, 555551, 5555551, 55555551, 555555551, 5555555551, 55555555551, 555555555551, 5555555555551, 55555555555551, 555555555555551, 5555555555555551, 55555555555555551, 555555555555555551, 5555555555555555551, 55555555555555555551, 555555555555555555551
OFFSET
1,2
COMMENTS
Primes up to n=100 are 555555555551 and 5555555555551; the next prime term has 609 digits (see A056684).
FORMULA
a(n) = 10*a(n-1) + 41 with a(0)=-4.
From Vincenzo Librandi, Jul 05 2012: (Start)
G.f.: x*(1+40*x)/((1-x)*(1-10*x)).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)
E.g.f.: 4 + exp(x)*(5*exp(9*x) - 41)/9. - Elmo R. Oliveira, Sep 09 2024
MATHEMATICA
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 *)
PROG
(Magma)[(5*10^n-41)/9: n in [1..20]]; // Vincenzo Librandi, Jul 05 2012
CROSSREFS
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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 25 2010
STATUS
approved