A309825 -id:A309825 - cp's OEIS frontend

A309819 Digits of the 10-adic integer (987654321/(1-10^9))^(1/7).

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

Offset: 0

Seiichi Manyama, Aug 18 2019

x = ...612123123752627210431674758928842961.

x^7 = ...987654321987654321987654321987654321.

			          1^7 == 1         (mod 10).
         61^7 == 21        (mod 10^2).
        961^7 == 321       (mod 10^3).
       2961^7 == 4321      (mod 10^4).
      42961^7 == 54321     (mod 10^5).
     842961^7 == 654321    (mod 10^6).
    8842961^7 == 7654321   (mod 10^7).
   28842961^7 == 87654321  (mod 10^8).
  928842961^7 == 987654321 (mod 10^9).

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

Digits of the 10-adic integer (987654321/(1-10^9))^(1/k): A309818 (k=3), this sequence (k=7), A309820 (k=9).

Cf. A010888, A138531, A309822, A309825.

N=100; M=987654321/(1-10^9); Vecrev(digits(lift(chinese(Mod((M+O(2^N))^(1/7), 2^N), Mod((M+O(5^N))^(1/7), 5^N)))), N)

A309824 Digits of the 10-adic integer (2345678987654321/(1-10^16))^(1/3).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Aug 18 2019

x = ...068250451956420480608557871517841.

x^3 = ...123456789876543212345678987654321.

			                  1^3 == 1                 (mod 10).
                 41^3 == 21                (mod 10^2).
                841^3 == 321               (mod 10^3).
               7841^3 == 4321              (mod 10^4).
              17841^3 == 54321             (mod 10^5).
             517841^3 == 654321            (mod 10^6).
            1517841^3 == 7654321           (mod 10^7).
           71517841^3 == 87654321          (mod 10^8).
          871517841^3 == 987654321         (mod 10^9).
         7871517841^3 == 8987654321        (mod 10^10).
        57871517841^3 == 78987654321       (mod 10^11).
       557871517841^3 == 678987654321      (mod 10^12).
      8557871517841^3 == 5678987654321     (mod 10^13).
      8557871517841^3 == 45678987654321    (mod 10^14).
    608557871517841^3 == 345678987654321   (mod 10^15).
    608557871517841^3 == 2345678987654321  (mod 10^16).
  80608557871517841^3 == 12345678987654321 (mod 10^17).

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

Digits of the 10-adic integer (2345678987654321/(1-10^16))^(1/k): this sequence (k=3), A309825 (k=7), A309826 (k=9).

Cf. A309818.

N=100; M=2345678987654321/(1-10^16); Vecrev(digits(lift(chinese(Mod((M+O(2^N))^(1/3), 2^N), Mod((M+O(5^N))^(1/3), 5^N)))), N)

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

Original entry on oeis.org

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

Seiichi Manyama, Aug 18 2019

x = ...906427851104463968866729914840881.

x^9 = ...123456789876543212345678987654321.

			                  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).

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

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

Cf. A309820.

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)

cp's OEIS Frontend

A309819 Digits of the 10-adic integer (987654321/(1-10^9))^(1/7).

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A309824 Digits of the 10-adic integer (2345678987654321/(1-10^16))^(1/3).

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

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PARI