A309644 Digits of the 10-adic integer (-43/9)^(1/3).

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

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: A369235 A110793 A199290 * A001903 A011345 A201770

Adjacent sequences: A309641 A309642 A309643 * A309645 A309646 A309647

Keyword

nonn,base

Author

Seiichi Manyama, Aug 11 2019

Status

approved