A056684 -id:A056684 - cp's OEIS frontend

A104517 Number of distinct prime divisors of 55...1 (with n 5s).

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

Offset: 1

Parthasarathy Nambi, Apr 19 2005

Number of distinct prime factors of (10^(n + 1) - 1)*5/9 - 4. - Stefan Steinerberger, Mar 06 2006

			The number of distinct prime divisors of 51 is 2 which is the first term in the sequence.
The number of distinct prime divisors of 551 is 2 which is the second term in the sequence.
The number of distinct prime divisors of 5551 is 3 which is the third term in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..200

Cf. A001221, A056684 (a(n)=1), A104484, A173804.

[#PrimeDivisors((10^(n+1)-1)*5 div 9-4): n in [1..80]]; // Vincenzo Librandi, Mar 09 2018

f:= n -> nops(numtheory:-factorset( (10^(n + 1) - 1)*5/9 - 4)):
map(f, [$1..92]); # Robert Israel, Mar 08 2018

Table[Length[FactorInteger[(10^(n + 1) - 1)*5/9 - 4]], {n, 1, 50}] (* Stefan Steinerberger, Mar 06 2006 *)

a(n) = omega((10^(n + 1) - 1)*5/9 - 4); \\ Michel Marcus, Mar 09 2018

a(n) = A001221(A173804(n+1)). - Amiram Eldar, Jan 24 2020

More terms from Stefan Steinerberger, Mar 06 2006

a(51)-a(92), and offset corrected, by Robert Israel, Mar 08 2018

A173804 a(n) = (5*10^n - 41)/9 for n > 0.

Original entry on oeis.org

1, 51, 551, 5551, 55551, 555551, 5555551, 55555551, 555555551, 5555555551, 55555555551, 555555555551, 5555555555551, 55555555555551, 555555555555551, 5555555555555551, 55555555555555551, 555555555555555551, 5555555555555555551, 55555555555555555551, 555555555555555555551

Offset: 1

Vincenzo Librandi, Feb 25 2010

Primes up to n=100 are 555555555551 and 5555555555551; the next prime term has 609 digits (see A056684).

Vincenzo Librandi, Table of n, a(n) for n = 1..100
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A056684 (numbers n such that (5*10^(n+1)-41)/9 is prime). - Klaus Brockhaus, Feb 28 2010

[(5*10^n-41)/9: n in [1..20]]; // Vincenzo Librandi, Jul 05 2012

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 *)

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

A099415 Numbers k such that 5*R_k - 4 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

12, 13, 609

Offset: 1

Robert G. Wilson v, Oct 14 2004

Also numbers k such that (5*10^k - 41)/9 is prime.

a(4) > 10^5. - Robert Price, Nov 16 2014

Makoto Kamada, Prime numbers of the form 55...551.
Index entries for primes involving repunits

Cf. A002275, A056684.

[n: n in [0..500] | IsPrime((5*10^n-41) div 9)]; // Vincenzo Librandi, Nov 17 2014

A099415:=n->`if`(isprime((5*10^n-41)/9), n, NULL): seq(A099415(n), n=1..10^3); # Wesley Ivan Hurt, Nov 16 2014

Do[ If[ PrimeQ[ 5(10^n - 1)/9 - 4], Print[n]], {n, 15000}]
Select[Range[10000], PrimeQ[(5 10^# - 41) / 9] &] (* Vincenzo Librandi, Nov 17 2014 *)

a(n) = A056684(n) + 1. - Robert Price, Nov 17 2014

cp's OEIS Frontend

A104517 Number of distinct prime divisors of 55...1 (with n 5s).

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A173804 a(n) = (5*10^n - 41)/9 for n > 0.

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A099415 Numbers k such that 5*R_k - 4 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

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