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A178769
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a(n) = (5*10^n + 13)/9.
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3
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2, 7, 57, 557, 5557, 55557, 555557, 5555557, 55555557, 555555557, 5555555557, 55555555557, 555555555557, 5555555555557, 55555555555557, 555555555555557, 5555555555555557, 55555555555555557, 555555555555555557
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n)^(4*k+2) + 1 == 0 (mod 250) for n>1, k>=0.
G.f.: (2-15*x)/((1-x)*(1-10*x)).
a(n) - 11*a(n-1) + 10*a(n-2) = 0 (n>1).
a(n) = a(n-1) + 5*10^(n-1) = 10*a(n-1) - 13 for n>0.
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MATHEMATICA
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CoefficientList[Series[(2 - 15 x) / ((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{11, -10}, {2, 7}, 20] (* Harvey P. Dale, Feb 28 2017 *)
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PROG
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(PARI) vector(20, n, n--; (5*10^n+13)/9) \\ G. C. Greubel, Jan 24 2019
(Sage) [(5*10^n+13)/9 for n in (0..20)] # G. C. Greubel, Jan 24 2019
(GAP) List([0..20], n -> (5*10^n+13)/9); # G. C. Greubel, Jan 24 2019
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CROSSREFS
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Cf. A165246 (..17, 117, 1117,..), A173193 (..27, 227, 2227,..), A173766 (..37, 337, 3337,..), A173772 (..47, 447, 4447,..), A067275 (..67, 667, 6667,..), A002281 (..77, 777, 7777,..), A173812 (..87, 887, 8887,..), A173833 (..97, 997, 9997,..).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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