A309606 - OEIS

A309606

Digits of the 10-adic integer (-7/3)^(1/3).

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

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OFFSET

0,4

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

EXAMPLE

1^3 == 1 (mod 10).

11^3 == 31 (mod 10^2).

11^3 == 331 (mod 10^3).

4011^3 == 3331 (mod 10^4).

64011^3 == 33331 (mod 10^5).

764011^3 == 333331 (mod 10^6).

MAPLE

op([1, 3], padic:-rootp(x^3+7/3, 10, 100)); # Robert Israel, Aug 09 2019

PROG

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((-7/3+O(2^N))^(1/3), 2^N), Mod((-7/3+O(5^N))^(1/3), 5^N)))), N)

(Ruby)