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A309722 Digits of the 4-adic integer (1/3)^(1/3). 3
3, 0, 3, 2, 1, 1, 0, 1, 2, 2, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 2, 3, 2, 2, 3, 2, 3, 3, 1, 1, 2, 0, 1, 3, 0, 0, 2, 3, 2, 2, 2, 0, 0, 0, 0, 0, 3, 2, 0, 2, 0, 2, 0, 0, 2, 3, 2, 3, 2, 2, 3, 3, 2, 2, 2, 0, 2, 3, 1, 0, 0, 3, 3, 2, 3, 3, 3, 0, 3, 1, 3, 2, 3, 2, 2, 1, 2, 0, 3, 2, 0, 2, 3, 0, 0, 2, 0, 3, 3, 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) = 3, b(n) = b(n-1) + 3 * (3 * b(n-1)^3 - 1) mod 4^n for n > 1, then a(n) = (b(n+1) - b(n))/4^n.
PROG
(PARI) N=100; Vecrev(digits(lift((1/3+O(2^(2*N)))^(1/3)), 4), N)
(Ruby)
def A309722(n)
ary = [3]
a = 3
n.times{|i|
b = (a + 3 * (3 * a ** 3 - 1)) % (4 ** (i + 2))
ary << (b - a) / (4 ** (i + 1))
a = b
}
ary
end
p A309722(100)
CROSSREFS
Digits of the k-adic integer (1/(k-1))^(1/(k-1)): this sequence (k=4), A309723 (k=6), A309724 (k=8), A225464 (k=10).
Sequence in context: A171911 A180193 A229964 * A070298 A024938 A332715
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Aug 14 2019
STATUS
approved

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Last modified July 24 22:37 EDT 2024. Contains 374585 sequences. (Running on oeis4.)