A173772 -id:A173772 - 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

A104889 Number of distinct prime divisors of 44...447 (with n 4s).

Original entry on oeis.org

1, 2, 1, 2, 3, 2, 2, 4, 1, 3, 2, 3, 2, 2, 2, 2, 3, 3, 1, 5, 4, 4, 4, 7, 1, 4, 2, 5, 3, 3, 3, 3, 3, 6, 4, 5, 3, 2, 3, 5, 6, 7, 4, 4, 4, 2, 5, 3, 3, 6, 4, 6, 2, 5, 3, 5, 3, 6, 4, 6, 4, 6, 3, 5, 6, 6, 4, 5, 2, 4, 7, 7, 3, 5, 3, 3, 3, 5, 4, 10, 5, 4, 3, 5, 3, 2, 4

Offset: 1

Parthasarathy Nambi, Apr 24 2005

nonn

Also number of distinct prime factors of (10^(n + 1) - 1)*4/9 + 3. - Stefan Steinerberger, Feb 21 2006

			Number of distinct prime divisors of 47 is 1 (prime).
Number of distinct prime divisors of 447 is 2.
Number of distinct prime divisors of 4447 is 1 (prime).

Amiram Eldar, Table of n, a(n) for n = 1..201

Cf. A001221, A104564, A173772.

Table[Length[FactorInteger[(10^(n + 1) - 1)*4/9 + 3]], {n, 1, 40}] (* Stefan Steinerberger, Feb 21 2006 *)

a(n) = A001221(A173772(n+1)). - Amiram Eldar, Jan 27 2020

More terms from Stefan Steinerberger, Feb 21 2006

Offset corrected and more terms added by Amiram Eldar, Jan 27 2020

A309609 Digits of the 10-adic integer (23/9)^(1/3).

Original entry on oeis.org

3, 6, 2, 9, 7, 6, 0, 4, 7, 4, 2, 3, 4, 9, 0, 2, 1, 6, 5, 5, 4, 5, 9, 7, 3, 3, 2, 6, 4, 9, 6, 0, 0, 6, 4, 9, 5, 3, 2, 3, 1, 9, 6, 3, 3, 0, 5, 6, 1, 1, 4, 7, 2, 3, 1, 6, 2, 5, 7, 9, 9, 7, 3, 5, 1, 0, 8, 4, 2, 0, 2, 6, 3, 1, 6, 8, 2, 6, 4, 8, 4, 3, 4, 5, 9, 5, 3, 8, 9, 8, 6, 5, 7, 9, 1, 7, 2, 7, 6, 1

Offset: 0

Seiichi Manyama, Aug 10 2019

			       3^3 == 7      (mod 10).
      63^3 == 47     (mod 10^2).
     263^3 == 447    (mod 10^3).
    9263^3 == 4447   (mod 10^4).
   79263^3 == 44447  (mod 10^5).
  679263^3 == 444447 (mod 10^6).

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A173772, A309600, A309612.

N=100; Vecrev(digits(lift(chinese(Mod((23/9+O(2^N))^(1/3), 2^N), Mod((23/9+O(5^N))^(1/3), 5^N)))), N)

def A309609(n)
  ary = [3]
  a = 3
  n.times{|i|
    b = (a + 3 * (9 * a ** 3 - 23)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309609(100)

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 - 23) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n

A173771 Primes of form (4*10^n+23)/9.

Original entry on oeis.org

3, 7, 47, 4447, 4444444447, 44444444444444444447, 44444444444444444444444447

Offset: 1

Vincenzo Librandi, Feb 24 2010

nonn

a(9) has 1310 digits. - Bruno Berselli, Jul 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..8

Cf. A173772
Equals 3 followed by A092480 (primes of the form 40*R_n + 7). - Klaus Brockhaus and R. J. Mathar, Feb 27 2010
Cf. A056682.

[a: n in [0..100] | IsPrime(a) where a is (4*10^n+23)div 9 ]; // Vincenzo Librandi, Jul 26 2012

Select[Table[(4*10^n+23)/9,{n,0,100}],PrimeQ] (* Vincenzo Librandi, Jul 26 2012 *)

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

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A104889 Number of distinct prime divisors of 44...447 (with n 4s).

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A309609 Digits of the 10-adic integer (23/9)^(1/3).

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A173771 Primes of form (4*10^n+23)/9.

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Magma

Mathematica