A322932 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A322932

Digits of the 8-adic integer 5^(1/3).

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

(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 * (b(n-1)^3 - 5) mod 8^n for n > 1, then a(n) = (b(n+1) - b(n))/8^n. - Seiichi Manyama, Aug 14 2019

EXAMPLE

20447135^3 == 5 (mod 8^8) in octal.

PROG

(PARI) N=100; Vecrev(digits(lift((5+O(2^(3*N)))^(1/3)), 8), N) \\ Seiichi Manyama, Aug 14 2019

(Ruby)

def A322932(n)

ary = [5]

a = 5

n.times{|i|

b = (a + 5 * (a ** 3 - 5)) % (8 ** (i + 2))

ary << (b - a) / (8 ** (i + 1))

a = b