A309723 - OEIS

A309723

Digits of the 6-adic integer (1/5)^(1/5).

5, 0, 4, 5, 5, 1, 5, 4, 1, 2, 0, 3, 5, 3, 2, 5, 0, 0, 5, 4, 5, 3, 0, 3, 4, 2, 0, 0, 1, 4, 0, 0, 1, 2, 2, 3, 3, 4, 5, 4, 4, 5, 3, 1, 1, 5, 2, 0, 5, 4, 2, 2, 5, 4, 0, 2, 5, 5, 4, 2, 1, 1, 4, 2, 2, 4, 5, 4, 1, 5, 0, 1, 0, 4, 2, 1, 3, 4, 0, 1, 2, 0, 0, 3, 3, 1, 3, 4, 2, 3, 4, 2, 5, 0, 3, 3, 0, 1, 2, 0, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Wikipedia, Hensel's Lemma.

FORMULA

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 5, b(n) = b(n-1) + 5 * (5 * b(n-1)^5 - 1) mod 6^n for n > 1, then a(n) = (b(n+1) - b(n))/6^n.

PROG

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((1/5+O(2^N))^(1/5), 2^N), Mod((1/5+O(3^N))^(1/5), 3^N))), 6), N)

(Ruby)

def A309723(n)

ary = [5]

a = 5

n.times{|i|

b = (a + 5 * (5 * a ** 5 - 1)) % (6 ** (i + 2))

ary << (b - a) / (6 ** (i + 1))

a = b

}

ary