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A309644 Digits of the 10-adic integer (-43/9)^(1/3). 3
7, 9, 3, 1, 4, 9, 2, 8, 3, 0, 0, 0, 8, 2, 6, 1, 4, 3, 7, 0, 1, 8, 9, 0, 3, 1, 6, 9, 4, 8, 4, 8, 4, 2, 2, 8, 8, 4, 0, 0, 0, 0, 8, 7, 0, 0, 7, 8, 9, 6, 3, 0, 0, 4, 0, 5, 9, 4, 6, 9, 6, 9, 2, 0, 1, 8, 5, 3, 2, 0, 1, 2, 0, 5, 7, 9, 3, 3, 9, 4, 5, 6, 2, 0, 3, 1, 3, 5, 1, 4, 0, 5, 8, 2, 5, 7, 2, 6, 4, 9 (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) = 7, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 43) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

EXAMPLE

       7^3 == 3      (mod 10).

      97^3 == 73     (mod 10^2).

     397^3 == 773    (mod 10^3).

    1397^3 == 7773   (mod 10^4).

   41397^3 == 77773  (mod 10^5).

  941397^3 == 777773 (mod 10^6).

PROG

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((-43/9+O(2^N))^(1/3), 2^N), Mod((-43/9+O(5^N))^(1/3), 5^N)))), N)

(Ruby)

def A309644(n)

  ary = [7]

  a = 7

  n.times{|i|

    b = (a + 3 * (9 * a ** 3 + 43)) % (10 ** (i + 2))

    ary << (b - a) / (10 ** (i + 1))

    a = b

  }

  ary

end

p A309644(100)

CROSSREFS

Cf. A309600, A309604.

Sequence in context: A249546 A110793 A199290 * A001903 A011345 A201770

Adjacent sequences:  A309641 A309642 A309643 * A309645 A309646 A309647

KEYWORD

nonn,base

AUTHOR

Seiichi Manyama, Aug 11 2019

STATUS

approved

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Last modified February 25 11:51 EST 2020. Contains 332233 sequences. (Running on oeis4.)