A309570 - OEIS

A309570

Digits of the 10-adic integer (17/3)^(1/3).

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

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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) = 9, b(n) = b(n-1) + 3 * b(n-1)^3 - 17 mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

EXAMPLE

9^3 == 9 (mod 10).

79^3 == 39 (mod 10^2).

179^3 == 339 (mod 10^3).

6179^3 == 3339 (mod 10^4).

26179^3 == 33339 (mod 10^5).

826179^3 == 333339 (mod 10^6).

PROG

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((17/3+O(2^N))^(1/3), 2^N), Mod((17/3+O(5^N))^(1/3), 5^N)))), N)

(Ruby)

def A309570(n)

ary = [9]