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A309595 Digits of the 10-adic integer (-31/9)^(1/3). 3
1, 8, 0, 1, 1, 8, 6, 6, 4, 1, 6, 0, 3, 9, 9, 0, 9, 3, 8, 0, 7, 1, 6, 5, 5, 2, 0, 8, 8, 4, 6, 7, 9, 8, 3, 0, 6, 7, 0, 7, 4, 0, 5, 9, 9, 5, 2, 0, 6, 7, 8, 9, 7, 8, 7, 2, 1, 2, 0, 7, 4, 8, 8, 4, 3, 6, 0, 6, 8, 2, 1, 4, 2, 8, 6, 7, 0, 5, 7, 4, 9, 7, 7, 5, 8, 4, 5, 9, 5, 7, 8, 4, 7, 9, 4, 4, 3, 7, 9, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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) = 1, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 + 31) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

EXAMPLE

       1^3 == 1      (mod 10).

      81^3 == 41     (mod 10^2).

      81^3 == 441    (mod 10^3).

    1081^3 == 4441   (mod 10^4).

   11081^3 == 44441  (mod 10^5).

  811081^3 == 444441 (mod 10^6).

PROG

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((-31/9+O(2^N))^(1/3), 2^N), Mod((-31/9+O(5^N))^(1/3), 5^N)))), N)

(Ruby)

def A309595(n)

  ary = [1]

  a = 1

  n.times{|i|

    b = (a + 7 * (9 * a ** 3 + 31)) % (10 ** (i + 2))

    ary << (b - a) / (10 ** (i + 1))

    a = b

  }

  ary

end

p A309595(100)

CROSSREFS

Cf. A173768, A309600, A309614.

Sequence in context: A054373 A061847 A307224 * A329074 A296434 A164790

Adjacent sequences:  A309592 A309593 A309594 * A309596 A309597 A309598

KEYWORD

nonn,base

AUTHOR

Seiichi Manyama, Aug 10 2019

STATUS

approved

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Last modified February 21 23:41 EST 2020. Contains 332113 sequences. (Running on oeis4.)