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A327305
Digits of one of the two 5-adic integers sqrt(-9) that is related to A327303.
4
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
OFFSET
0,1
COMMENTS
This is the 5-adic solution to x^2 = -9 that ends in 4. A327304 gives the other solution that ends in 1.
LINKS
G. P. Michon, Introduction to p-adic integers, Numericana.
FORMULA
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).
a(n) = (A327303(n+1) - A327303(n))/5^n.
For n > 0, a(n) = 4 - A327304(n).
EXAMPLE
Equals ...1131142000414124220322114423220241100304.
MAPLE
op([1, 1, 3], select(t -> padic:-ratvaluep(t, 1)=4, [padic:-rootp(x^2+9, 5, 100)])); # Robert Israel, Aug 31 2020
PROG
(PARI) a(n) = truncate(-sqrt(-9+O(5^(n+1))))\5^n
CROSSREFS
Digits of 5-adic square roots:
A327304, this sequence (sqrt(-9));
A324029, A324030 (sqrt(-6));
A269591, A269592 (sqrt(-4));
A210850, A210851 (sqrt(-1));
A324025, A324026 (sqrt(6)).
Sequence in context: A283572 A057075 A281653 * A290328 A200682 A263618
KEYWORD
nonn,base
AUTHOR
Jianing Song, Sep 16 2019
STATUS
approved