A309826 Digits of the 10-adic integer (2345678987654321/(1-10^16))^(1/9).

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

Offset

0,2

Comments

x = ...906427851104463968866729914840881.

x^9 = ...123456789876543212345678987654321.

Links

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

Example

                  1^9 == 1                 (mod 10).
                 81^9 == 21                (mod 10^2).
                881^9 == 321               (mod 10^3).
                881^9 == 4321              (mod 10^4).
              40881^9 == 54321             (mod 10^5).
             840881^9 == 654321            (mod 10^6).
            4840881^9 == 7654321           (mod 10^7).
           14840881^9 == 87654321          (mod 10^8).
          914840881^9 == 987654321         (mod 10^9).
         9914840881^9 == 8987654321        (mod 10^10).
        29914840881^9 == 78987654321       (mod 10^11).
       729914840881^9 == 678987654321      (mod 10^12).
      6729914840881^9 == 5678987654321     (mod 10^13).
     66729914840881^9 == 45678987654321    (mod 10^14).
    866729914840881^9 == 345678987654321   (mod 10^15).
   8866729914840881^9 == 2345678987654321  (mod 10^16).
  68866729914840881^9 == 12345678987654321 (mod 10^17).

Prog

(PARI) N=100; M=2345678987654321/(1-10^16); Vecrev(digits(lift(chinese(Mod((M+O(2^N))^(1/9), 2^N), Mod((M+O(5^N))^(1/9), 5^N)))), N)

Crossrefs

Digits of the 10-adic integer (2345678987654321/(1-10^16))^(1/k): A309824 (k=3), A309825 (k=7), this sequence (k=9).

Cf. A309820.

Sequence in context: A113809 A231097 A309820 * A321096 A345746 A243508

Adjacent sequences: A309823 A309824 A309825 * A309827 A309828 A309829

Keyword

nonn,base

Author

Seiichi Manyama, Aug 18 2019

Status

approved