A173833 -id:A173833 - cp's OEIS frontend

A086947 Numbers k such that R(k+9) = 3.

21, 291, 2991, 29991, 299991, 2999991, 29999991, 299999991, 2999999991, 29999999991, 299999999991, 2999999999991, 29999999999991, 299999999999991, 2999999999999991, 29999999999999991, 299999999999999991, 2999999999999999991, 29999999999999999991, 299999999999999999991

Offset: 1

Ray Chandler, Jul 24 2003

If k is in this sequence then Reverse(k) = (2/3)*k - 2. Also A101703 is the sequence of all numbers k such that Reverse(k) = (2/3)*k - 2. So this sequence is a subsequence of A101703. - Farideh Firoozbakht, Dec 30 2004

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A004086, A085331, A086948, A101700, A101703, A173833.

[3*(10^n-3): n in [1..25] ]; // Vincenzo Librandi, Aug 22 2011

Table[3*(10^n-3), {n, 17}]
Table[FromDigits[PadRight[{3},n,0]],{n,2,20}]-9 (* Harvey P. Dale, Nov 27 2012 *)

a(n) = 3*(10^n - 3).
R(a(n)) = A086948(n).
From Chai Wah Wu, Aug 01 2020: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2.
G.f.: x*(60*x + 21)/((x - 1)*(10*x - 1)). (End)
From Elmo R. Oliveira, May 01 2025: (Start)
E.g.f.: 3*(2 - 3*exp(x) + exp(10*x)).
a(n) = 3*A173833(n). (End)

A105068 Number of distinct prime divisors of 10^n - 3.

Original entry on oeis.org

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

Offset: 1

Parthasarathy Nambi, Apr 05 2005

nonn

			If n = 1, 2 or 3, then 10^n - 3 is prime and thus the first three terms are 1.

Amiram Eldar, Table of n, a(n) for n = 1..121

Cf. A001221, A173833.

Table[Length[FactorInteger[10^n - 3]], {n, 1, 50}] (* Stefan Steinerberger, Feb 21 2006 *)

a(n) = A001221(A173833(n)). - Amiram Eldar, Jan 25 2020

More terms from Stefan Steinerberger, Feb 21 2006

More terms from Amiram Eldar, Jan 25 2020

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

Original entry on oeis.org

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

A086946 Numbers k such that R(k+6) = 2.

Original entry on oeis.org

14, 194, 1994, 19994, 199994, 1999994, 19999994, 199999994, 1999999994, 19999999994, 199999999994, 1999999999994, 19999999999994, 199999999999994, 1999999999999994, 19999999999999994, 199999999999999994, 1999999999999999994, 19999999999999999994, 199999999999999999994

Offset: 1

Ray Chandler, Jul 24 2003

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A004086, A086949, A173833.

[2*(10^n-3): n in [1..25] ]; // Vincenzo Librandi, Aug 22 2011

a(n) = 2*(10^n - 3).
R(a(n)) = A086949(n).
From Stefano Spezia, Dec 15 2022: (Start)
O.g.f.: 2*x*(7 + 20*x)/((1 - x)*(1 - 10*x)).
E.g.f.: 2*(2 - 3*exp(x) + exp(10*x)).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)
a(n) = 2*A173833(n). - Elmo R. Oliveira, May 02 2025

A177079 a(n) = 5*(10^n - 3).

Original entry on oeis.org

35, 485, 4985, 49985, 499985, 4999985, 49999985, 499999985, 4999999985, 49999999985, 499999999985, 4999999999985, 49999999999985, 499999999999985, 4999999999999985, 49999999999999985, 499999999999999985, 4999999999999999985, 49999999999999999985, 499999999999999999985

Offset: 1

Vincenzo Librandi

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A173833.

Magma
```
[5*(10^n-3): n in [1..35]];
```

Table[5*(10^n-3),{n,20}]; (* Alonso del Arte, Nov 15 2010 *)
LinearRecurrence[{11,-10},{35,485},20] (* Harvey P. Dale, Aug 20 2023 *)

a(n)=5*10^n-15 \\ Charles R Greathouse IV, Jun 04 2011

From Elmo R. Oliveira, Jun 12 2025: (Start)
G.f.: 5*x*(20*x+7)/((x-1)*(10*x-1)).
E.g.f.: 5*(2 - 3*exp(x) + exp(10*x)).
a(n) = 5*A173833(n).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)

A177108 a(n) = 4*(10^n-3).

Original entry on oeis.org

28, 388, 3988, 39988, 399988, 3999988, 39999988, 399999988, 3999999988, 39999999988, 399999999988, 3999999999988, 39999999999988, 399999999999988, 3999999999999988, 39999999999999988, 399999999999999988

Offset: 1

Vincenzo Librandi, Nov 15 2010

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (11,-10).

[4*(10^n-3): n in [1..20]]; // Vincenzo Librandi, Jul 15 2012

CoefficientList[Series[4*(7+20*x)/((10*x-1)*(x-1)),{x,0,40}],x] (* Vincenzo Librandi, Jul 15 2012 *)
4(10^Range[20]-3) (* or *) LinearRecurrence[{11,-10},{28,388},20] (* Harvey P. Dale, Sep 25 2012 *)

G.f.: 4*x*(7+20*x) / ( (10*x-1)*(x-1) ). a(n)=4*A173833(n). - R. J. Mathar, Jan 06 2011

a(n) = a(n-1) +36*10^(n-1) = 10*a(n-1) +108 = 11*a(n-1) -10*a(n-2). - Vincenzo Librandi, Jul 15 2012

A240696 Prime numbers n such that replacing each digit d in the decimal expansion of n with its 9's complement produces a prime.

Original entry on oeis.org

2, 7, 97, 997, 99999999999999997

Offset: 1

Michel Lagneau, Apr 10 2014

a(n) = {2} union {primes of the form 10^n - 3} = {2} union {A093172}.
Primes p such that A061601(p) is also prime.
The next term has 140 digits.

			997 is in the sequence because 997 becomes (002) = 2, which is prime.

Cf. A093172, A173833.

lst={};f[n_]:=Block[{a=IntegerDigits[Prime[n]],b="",k=1,l},l=Length[a];While[k

cp's OEIS Frontend

A086947 Numbers k such that R(k+9) = 3.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A105068 Number of distinct prime divisors of 10^n - 3.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

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

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Mathematica

PARI

Sage

Formula

A086946 Numbers k such that R(k+6) = 2.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Formula

A177079 a(n) = 5*(10^n - 3).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A177108 a(n) = 4*(10^n-3).

Views

Author

Keywords

Links

Programs

Magma

Mathematica

Formula

A240696 Prime numbers n such that replacing each digit d in the decimal expansion of n with its 9's complement produces a prime.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica