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A309645 Digits of the 10-adic integer (11/9)^(1/3). 3
9, 5, 8, 6, 6, 5, 0, 7, 6, 0, 5, 1, 0, 8, 9, 4, 8, 5, 8, 5, 6, 2, 2, 5, 2, 1, 8, 7, 6, 9, 9, 8, 2, 3, 8, 1, 0, 5, 8, 5, 7, 0, 0, 9, 6, 7, 4, 2, 0, 6, 6, 7, 7, 1, 2, 4, 1, 7, 9, 1, 2, 5, 4, 8, 7, 7, 3, 4, 4, 9, 1, 7, 6, 9, 6, 7, 0, 7, 4, 1, 3, 3, 6, 9, 7, 4, 6, 9, 8, 8, 5, 9, 0, 0, 1, 5, 4, 0, 5, 4 (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) = 9, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 - 11) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

EXAMPLE

       9^3 == 9      (mod 10).

      59^3 == 79     (mod 10^2).

     859^3 == 779    (mod 10^3).

    6859^3 == 7779   (mod 10^4).

   66859^3 == 77779  (mod 10^5).

  566859^3 == 777779 (mod 10^6).

PROG

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((11/9+O(2^N))^(1/3), 2^N), Mod((11/9+O(5^N))^(1/3), 5^N)))), N)

(Ruby)

def A309645(n)

  ary = [9]

  a = 9

  n.times{|i|

    b = (a + 7 * (9 * a ** 3 - 11)) % (10 ** (i + 2))

    ary << (b - a) / (10 ** (i + 1))

    a = b

  }

  ary

end

p A309645(100)

CROSSREFS

Cf. A309600, A309603.

Sequence in context: A245292 A203081 A329715 * A146483 A090463 A272795

Adjacent sequences:  A309642 A309643 A309644 * A309646 A309647 A309648

KEYWORD

nonn,base

AUTHOR

Seiichi Manyama, Aug 11 2019

STATUS

approved

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Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)