A327305 Digits of one of the two 5-adic integers sqrt(-9) that is related to A327303.

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

Robert Israel, Table of n, a(n) for n = 0..10000

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

Cf. A327302, A327303.

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

Adjacent sequences: A327302 A327303 A327304 * A327306 A327307 A327308

Keyword

nonn,base

Author

Jianing Song, Sep 16 2019

Status

approved