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A309647 Digits of the 10-adic integer (-53/9)^(1/3). 2
7, 2, 6, 1, 3, 2, 9, 4, 6, 9, 1, 4, 6, 5, 1, 8, 6, 9, 0, 9, 6, 7, 0, 7, 6, 3, 6, 7, 5, 6, 4, 8, 4, 7, 0, 1, 9, 2, 3, 9, 6, 0, 0, 5, 7, 4, 6, 9, 6, 7, 9, 6, 7, 1, 7, 1, 2, 1, 6, 8, 9, 9, 5, 3, 5, 8, 1, 0, 5, 1, 4, 6, 4, 6, 2, 6, 8, 3, 2, 0, 8, 8, 1, 4, 9, 7, 4, 2, 3, 6, 1, 0, 5, 7, 2, 6, 9, 6, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 7, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 53) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
EXAMPLE
7^3 == 3 (mod 10).
27^3 == 83 (mod 10^2).
627^3 == 883 (mod 10^3).
1627^3 == 8883 (mod 10^4).
31627^3 == 88883 (mod 10^5).
231627^3 == 888883 (mod 10^6).
PROG
(PARI) N=100; Vecrev(digits(lift(chinese(Mod((-53/9+O(2^N))^(1/3), 2^N), Mod((-53/9+O(5^N))^(1/3), 5^N)))), N)
(Ruby)
def A309647(n)
ary = [7]
a = 7
n.times{|i|
b = (a + 3 * (9 * a ** 3 + 53)) % (10 ** (i + 2))
ary << (b - a) / (10 ** (i + 1))
a = b
}
ary
end
p A309647(100)
CROSSREFS
Sequence in context: A248285 A117029 A128475 * A225444 A175408 A019934
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Aug 11 2019
STATUS
approved

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Last modified May 20 02:14 EDT 2024. Contains 372703 sequences. (Running on oeis4.)