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A327305
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Digits of one of the two 5-adic integers sqrt(-9) that is related to A327303.
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4
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4, 0, 3, 0, 0, 1, 1, 4, 2, 0, 2, 2, 3, 2, 4, 4, 1, 1, 2, 2, 3, 0, 2, 2, 4, 2, 1, 4, 1, 4, 0, 0, 0, 2, 4, 1, 1, 3, 1, 1, 0, 4, 1, 2, 1, 2, 2, 1, 1, 2, 0, 0, 3, 1, 2, 0, 4, 2, 0, 3, 4, 4, 0, 0, 0, 0, 1, 4, 0, 3, 4, 0, 1, 4, 4, 3, 3, 0, 2, 3, 2, 3, 3, 3, 1, 4, 2, 4
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OFFSET
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0,1
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COMMENTS
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This is the 5-adic solution to x^2 = -9 that ends in 4. A327304 gives the other solution that ends in 1.
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LINKS
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FORMULA
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For n > 0, a(n) is the unique m in {0, 1, 2, 3, 4} such that (A327303(n) + m*5^n)^2 + 9 is divisible by 5^(n+1).
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EXAMPLE
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Equals ...1131142000414124220322114423220241100304.
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MAPLE
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op([1, 1, 3], select(t -> padic:-ratvaluep(t, 1)=4, [padic:-rootp(x^2+9, 5, 100)])); # Robert Israel, Aug 31 2020
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PROG
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(PARI) a(n) = truncate(-sqrt(-9+O(5^(n+1))))\5^n
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CROSSREFS
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Digits of 5-adic square roots:
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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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