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A309569 Digits of the 10-adic integer (11/3)^(1/3). 3
3, 3, 2, 2, 5, 8, 6, 8, 3, 1, 7, 3, 2, 6, 1, 0, 0, 1, 3, 2, 5, 3, 3, 5, 5, 5, 0, 8, 8, 9, 0, 9, 1, 7, 3, 2, 9, 4, 3, 9, 9, 8, 3, 3, 0, 1, 4, 2, 7, 6, 9, 5, 1, 5, 9, 3, 2, 5, 3, 7, 3, 1, 4, 8, 9, 7, 0, 1, 9, 1, 1, 4, 1, 4, 7, 4, 9, 0, 7, 7, 1, 2, 4, 9, 3, 4, 3, 8, 0, 8, 1, 8, 9, 8, 3, 5, 5, 1, 9, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

FORMULA

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + 9 * (3 * b(n-1)^3 - 11) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

EXAMPLE

       3^3 == 7      (mod 10).

      33^3 == 37     (mod 10^2).

     233^3 == 337    (mod 10^3).

    2233^3 == 3337   (mod 10^4).

   52233^3 == 33337  (mod 10^5).

  852233^3 == 333337 (mod 10^6).

PROG

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((11/3+O(2^N))^(1/3), 2^N), Mod((11/3+O(5^N))^(1/3), 5^N)))), N)

(Ruby)

def A309569(n)

  ary = [3]

  a = 3

  n.times{|i|

    b = (a + 9 * (3 * a ** 3 - 11)) % (10 ** (i + 2))

    ary << (b - a) / (10 ** (i + 1))

    a = b

  }

  ary

end

p A309569(100)

CROSSREFS

Cf. A173766, A309600, A309641.

Sequence in context: A007515 A293729 A319297 * A292600 A014967 A210851

Adjacent sequences:  A309566 A309567 A309568 * A309570 A309571 A309572

KEYWORD

nonn,base

AUTHOR

Seiichi Manyama, Aug 10 2019

STATUS

approved

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Last modified May 8 19:28 EDT 2021. Contains 343666 sequences. (Running on oeis4.)