A324029 Digits of one of the two 5-adic integers sqrt(-6) that is related to A324027.

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

Offset

0,1

Comments

This square root of -6 in the 5-adic field ends with digit 2. The other, A324030, ends with digit 3.

Links

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

Wikipedia, p-adic number

Formula

a(n) = (A324027(n+1) - A324027(n))/5^n.

For n > 0, a(n) = 4 - A324030(n).

Equals A210850*A324026 = A210851*A324025, where each A-number represents a 5-adic number.

Example

The solution to x^2 == -6 (mod 5^4) such that x == 2 (mod 5) is x == 162 (mod 5^4), and 162 is written as 1122 in quinary, so the first four terms are 2, 2, 1 and 1.

Prog

(PARI) a(n) = truncate(sqrt(-6+O(5^(n+1))))\5^n

Crossrefs

Cf. A324027, A324028.

Digits of 5-adic square roots:

this sequence, A324030 (sqrt(-6));

A269591, A269592 (sqrt(-4));

A210850, A210851 (sqrt(-1));

A324025, A324026 (sqrt(6)).

Sequence in context: A339352 A305825 A366780 * A334046 A136605 A165621

Adjacent sequences: A324026 A324027 A324028 * A324030 A324031 A324032

Keyword

nonn,base

Author

Jianing Song, Sep 07 2019

Status

approved