A327304 Digits of one of the two 5-adic integers sqrt(-9) that is related to A327302.

1, 4, 1, 4, 4, 3, 3, 0, 2, 4, 2, 2, 1, 2, 0, 0, 3, 3, 2, 2, 1, 4, 2, 2, 0, 2, 3, 0, 3, 0, 4, 4, 4, 2, 0, 3, 3, 1, 3, 3, 4, 0, 3, 2, 3, 2, 2, 3, 3, 2, 4, 4, 1, 3, 2, 4, 0, 2, 4, 1, 0, 0, 4, 4, 4, 4, 3, 0, 4, 1, 0, 4, 3, 0, 0, 1, 1, 4, 2, 1, 2, 1, 1, 1, 3, 0, 2, 0

Offset

0,2

Comments

This is the 5-adic solution to x^2 = -9 that ends in 1. A327305 gives the other solution that ends in 4.

Links

Table of n, a(n) for n=0..87.

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 (A327302(n) + m*5^n)^2 + 9 is divisible by 5^(n+1).

a(n) = (A327302(n+1) - A327302(n))/5^n.

For n > 0, a(n) = 4 - A327305(n).

Example

Equals ...3313302444030320224122330021224203344141.

Prog

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

Crossrefs

Cf. A327302, A327303.

Digits of 5-adic square roots:

this sequence, A327305 (sqrt(-9));

A324029, A324030 (sqrt(-6));

A269591, A269592 (sqrt(-4));

A210850, A210851 (sqrt(-1));

A324025, A324026 (sqrt(6)).

Sequence in context: A173259 A021711 A334487 * A117445 A145079 A196222

Adjacent sequences: A327301 A327302 A327303 * A327305 A327306 A327307

Keyword

nonn,base

Author

Jianing Song, Sep 16 2019

Status

approved