A173802 -id:A173802 - cp's OEIS frontend

A104518 Number of distinct prime divisors of 55...3 (with n 5s).

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

Offset: 1

Parthasarathy Nambi, Apr 19 2005

			The number of distinct prime divisors of 53 is 1 (prime) which is the first term in the sequence.
The number of distinct prime divisors of 553 is 2 which is the second term in the sequence.
The number of distinct prime divisors of 5553 is 2 which is the third term in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..199

Cf. A001221, A173802.

A104518 := proc(n) local x ;x := [3,seq(5,k=1..n)] ; add(op(i,x)*10^(i-1),i=1..nops(x)) ; numtheory[factorset](%) ; nops(%) ; end proc: # R. J. Mathar, Aug 24 2011

Table[PrimeNu[(50*10^n - 23)/9], {n, 0, 50}] (* G. C. Greubel, May 06 2017 *)

a(n) = A001221(A173802(n+1)). - R. J. Mathar, Aug 24 2011

More terms from Amiram Eldar, Jan 25 2020

A309612 Digits of the 10-adic integer (-23/9)^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 10 2019

			       7^3 == 3      (mod 10).
      37^3 == 53     (mod 10^2).
     737^3 == 553    (mod 10^3).
     737^3 == 5553   (mod 10^4).
   20737^3 == 55553  (mod 10^5).
  320737^3 == 555553 (mod 10^6).

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

Cf. A173802, A309600, A309609.

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 A309612(n)
  ary = [7]
  a = 7
  n.times{|i|
    b = (a + 3 * (9 * a ** 3 + 23)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309612(100)

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, 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

cp's OEIS Frontend

A104518 Number of distinct prime divisors of 55...3 (with n 5s).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions