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

Author

Jianing Song, Sep 16 2019

Keywords

• nonn
• base

Comments

This is the 5-adic solution to x^2 = -9 that ends in 4. A327304 gives the other solution that ends in 1.

Examples

			Equals ...1131142000414124220322114423220241100304.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• G. P. Michon, Introduction to p-adic integers, Numericana.

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)).

Programs

Maple

op([1,1,3], select(t -> padic:-ratvaluep(t,1)=4, [padic:-rootp(x^2+9,5,100)])); # Robert Israel, Aug 31 2020

PARI

a(n) = truncate(-sqrt(-9+O(5^(n+1))))\5^n

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).