A173812 -id:A173812 - cp's OEIS frontend

A178769 a(n) = (5*10^n + 13)/9.

2, 7, 57, 557, 5557, 55557, 555557, 5555557, 55555557, 555555557, 5555555557, 55555555557, 555555555557, 5555555555557, 55555555555557, 555555555555557, 5555555555555557, 55555555555555557, 555555555555555557, 5555555555555555557, 55555555555555555557, 555555555555555555557

Offset: 0

Bruno Berselli, Jun 13 2010

Bruno Berselli, Table of n, a(n) for n = 0..1000.
Bruno Berselli, A property that includes the numbers of the form 5..57.
Index entries for linear recurrences with constant coefficients, signature (11,-10).

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,..).

Cf. A093143.

List([0..20], n -> (5*10^n+13)/9); # G. C. Greubel, Jan 24 2019

[(5*10^n+13)/9: n in [0..20]]; // Vincenzo Librandi, Jun 06 2013

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 *)

vector(20, n, n--; (5*10^n+13)/9) \\ G. C. Greubel, Jan 24 2019

[(5*10^n+13)/9 for n in (0..20)] # G. C. Greubel, Jan 24 2019

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.
a(n) = 1 + Sum_{i=0..n} A093143(i). - Bruno Berselli, Feb 16 2015
E.g.f.: exp(x)*(5*exp(9*x) + 13)/9. - Elmo R. Oliveira, Sep 09 2024

A105248 Number of distinct prime divisors of 88...887 (with n 8's).

Original entry on oeis.org

1, 2, 1, 1, 2, 1, 3, 3, 1, 2, 3, 1, 3, 4, 4, 4, 4, 2, 3, 3, 4, 3, 2, 3, 2, 2, 3, 5, 5, 4, 3, 4, 2, 5, 6, 2, 5, 3, 2, 3, 3, 3, 3, 3, 4, 2, 4, 2, 5, 2, 3, 5, 3, 6, 4, 5, 2, 5, 4, 3, 3, 3, 4, 2, 5, 4, 4, 5, 5, 4, 5, 1, 3, 6, 4, 2, 2, 4, 3, 4, 5, 7, 6, 5, 4, 8, 4

Offset: 0

Parthasarathy Nambi, Apr 29 2005

			The number of distinct prime divisors of 87 is 2.
The number of distinct prime divisors of 887 is 1 (prime).
The number of distinct prime divisors of 8887 is 1 (prime).

Amiram Eldar, Table of n, a(n) for n = 0..199

Cf. A104524, A104889.

Table[PrimeNu[(8*10^(n + 1) - 17)/9], {n, 1, 50}] (* G. C. Greubel, May 21 2017 *)

a(n) = omega((8*10^(n+1)-17)/9); \\ Michel Marcus, Jan 27 2014

a(n) = A001221(A173812(n+1)). - Michel Marcus, Jan 27 2014

More terms from Brian Lauer (bel136(AT)psu.edu), Feb 23 2006
Corrected and extended by Michel Marcus, Jan 27 2014
More terms from Amiram Eldar, Jan 27 2020

cp's OEIS Frontend

A178769 a(n) = (5*10^n + 13)/9.

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