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A322932 Digits of the 8-adic integer 5^(1/3). 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
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
}
ary
end
p A322932(100) # Seiichi Manyama, Aug 14 2019
CROSSREFS
Sequence in context: A179975 A019926 A249538 * A259619 A111498 A092140
KEYWORD
nonn,base,easy
AUTHOR
Patrick A. Thomas, Dec 31 2018
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)