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A309608
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Digits of the 10-adic integer (-13/9)^(1/3).
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3
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7, 0, 3, 0, 3, 3, 7, 4, 3, 3, 4, 2, 5, 1, 7, 3, 8, 4, 7, 6, 4, 5, 0, 4, 8, 7, 8, 4, 6, 3, 0, 2, 8, 3, 2, 4, 4, 6, 2, 3, 5, 0, 4, 6, 8, 2, 0, 1, 9, 5, 5, 4, 2, 8, 7, 8, 6, 6, 5, 0, 8, 9, 8, 2, 3, 8, 0, 1, 9, 5, 8, 6, 2, 3, 2, 8, 7, 7, 9, 8, 8, 4, 5, 0, 7, 4, 7, 1, 0, 2, 4, 9, 0, 8, 5, 4, 5, 0, 2, 6
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OFFSET
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0,1
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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) = 7, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 13) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
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EXAMPLE
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7^3 == 3 (mod 10).
7^3 == 43 (mod 10^2).
307^3 == 443 (mod 10^3).
307^3 == 4443 (mod 10^4).
30307^3 == 44443 (mod 10^5).
330307^3 == 444443 (mod 10^6).
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PROG
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(PARI) N=100; Vecrev(digits(lift(chinese(Mod((-13/9+O(2^N))^(1/3), 2^N), Mod((-13/9+O(5^N))^(1/3), 5^N)))), N)
(Ruby)
ary = [7]
a = 7
n.times{|i|
b = (a + 3 * (9 * a ** 3 + 13)) % (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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