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A309604
Digits of the 10-adic integer (43/9)^(1/3).
3
3, 0, 6, 8, 5, 0, 7, 1, 6, 9, 9, 9, 1, 7, 3, 8, 5, 6, 2, 9, 8, 1, 0, 9, 6, 8, 3, 0, 5, 1, 5, 1, 5, 7, 7, 1, 1, 5, 9, 9, 9, 9, 1, 2, 9, 9, 2, 1, 0, 3, 6, 9, 9, 5, 9, 4, 0, 5, 3, 0, 3, 0, 7, 9, 8, 1, 4, 6, 7, 9, 8, 7, 9, 4, 2, 0, 6, 6, 0, 5, 4, 3, 7, 9, 6, 8, 6, 4, 8, 5, 9, 4, 1, 7, 4, 2, 7, 3, 5, 0
OFFSET
0,1
LINKS
FORMULA
Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 - 43) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
EXAMPLE
3^3 == 7 (mod 10).
3^3 == 27 (mod 10^2).
603^3 == 227 (mod 10^3).
8603^3 == 2227 (mod 10^4).
58603^3 == 22227 (mod 10^5).
58603^3 == 222227 (mod 10^6).
PROG
(PARI) N=100; Vecrev(digits(lift(chinese(Mod((43/9+O(2^N))^(1/3), 2^N), Mod((43/9+O(5^N))^(1/3), 5^N)))), N)
(Ruby)
def A309604(n)
ary = [3]
a = 3
n.times{|i|
b = (a + 3 * (9 * a ** 3 - 43)) % (10 ** (i + 2))
ary << (b - a) / (10 ** (i + 1))
a = b
}
ary
end
p A309604(100)
CROSSREFS
Sequence in context: A199055 A016598 A119583 * A244009 A321482 A182042
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 09 2019
STATUS
approved