A309612 Digits of the 10-adic integer (-23/9)^(1/3).

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

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 + 23) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n

Example

       7^3 == 3      (mod 10).
      37^3 == 53     (mod 10^2).
     737^3 == 553    (mod 10^3).
     737^3 == 5553   (mod 10^4).
   20737^3 == 55553  (mod 10^5).
  320737^3 == 555553 (mod 10^6).

Prog

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((-23/9+O(2^N))^(1/3), 2^N), Mod((-23/9+O(5^N))^(1/3), 5^N)))), N)
(Ruby)
def A309612(n)
  ary = [7]
  a = 7
  n.times{|i|
    b = (a + 3 * (9 * a ** 3 + 23)) % (10 ** (i + 2))
    ary << (b - a) / (10 ** (i + 1))
    a = b
  }
  ary
end
p A309612(100)

Crossrefs

Cf. A173802, A309600, A309609.

Sequence in context: A050009 A173182 A253891 * A021856 A259453 A096715

Adjacent sequences: A309609 A309610 A309611 * A309613 A309614 A309615

Keyword

nonn,base

Author

Seiichi Manyama, Aug 10 2019

Status

approved