A309605 - OEIS

A309605

Digits of the 10-adic integer (61/9)^(1/3).

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

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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) + 7 * (9 * b(n-1)^3 - 61) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

EXAMPLE

9^3 == 9 (mod 10).

9^3 == 29 (mod 10^2).

509^3 == 229 (mod 10^3).

509^3 == 2229 (mod 10^4).

50509^3 == 22229 (mod 10^5).

450509^3 == 222229 (mod 10^6).

PROG

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((61/9+O(2^N))^(1/3), 2^N), Mod((61/9+O(5^N))^(1/3), 5^N)))), N)

(Ruby)

def A309605(n)

ary = [9]