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A225464
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10-adic integer x such that x^9 = 1/9.
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4
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9, 0, 6, 5, 1, 4, 8, 8, 0, 6, 4, 1, 3, 1, 2, 9, 1, 6, 1, 5, 4, 7, 3, 1, 2, 7, 1, 7, 4, 1, 0, 1, 7, 9, 4, 9, 1, 2, 5, 6, 3, 3, 0, 5, 5, 6, 3, 7, 7, 1, 9, 7, 7, 6, 2, 4, 7, 9, 4, 4, 3, 0, 7, 1, 7, 2, 8, 2, 8, 9, 1, 9, 3, 6, 9, 1, 1, 1, 3, 2, 3, 2, 4, 2, 5, 0, 1, 8, 4, 4, 7, 8, 2, 9, 6, 8, 3, 9, 3, 0
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OFFSET
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0,1
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COMMENTS
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This is the 10's complement of A225455.
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LINKS
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FORMULA
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Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 9 * (9 * b(n-1)^9 - 1) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. - Seiichi Manyama, Aug 14 2019
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EXAMPLE
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9^9 == -1 (mod 10).
9^9 == -11 (mod 10^2).
609^9 == -111 (mod 10^3).
5609^9 == -1111 (mod 10^4).
15609^9 == -11111 (mod 10^5).
415609^9 == -111111 (mod 10^6).
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PROG
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(PARI) n=0; for(i=1, 100, m=(8*(10^i-1)/9)+1; for(x=0, 9, if(((n+(x*10^(i-1)))^9)%(10^i)==m, n=n+(x*10^(i-1)); print1(x", "); break)))
(PARI) N=100; Vecrev(digits(lift(chinese(Mod((1/9+O(2^N))^(1/9), 2^N), Mod((1/9+O(5^N))^(1/9), 5^N)))), N) \\ Seiichi Manyama, Aug 07 2019
(Ruby)
ary = [9]
a = 9
n.times{|i|
b = (a + 9 * (9 * a ** 9 - 1)) % (10 ** (i + 2))
ary << (b - a) / (10 ** (i + 1))
a = b
}
ary
end
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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