A324030 Digits of one of the two 5-adic integers sqrt(-6) that is related to A324028.

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

Offset

0,1

Comments

This square root of -6 in the 5-adic field ends with digit 3. The other, A324029, ends with digit 2.

Links

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

Wikipedia, p-adic number

Formula

a(n) = (A324028(n+1) - A324028(n))/5^n.

For n > 0, a(n) = 4 - A324029(n).

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

Example

The solution to x^2 == -6 (mod 5^4) such that x == 3 (mod 5) is x == 463 (mod 5^4), and 463 is written as 3323 in quinary, so the first four terms are 3, 2, 3 and 3.

Prog

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

Crossrefs

Cf. A324027, A324028.

Digits of 5-adic square roots:

A324029, sequence (sqrt(-6));

A269591, A269592 (sqrt(-4));

A210850, A210851 (sqrt(-1));

A324025, A324026 (sqrt(6)).

Sequence in context: A370903 A153092 A165601 * A275821 A291674 A265157

Adjacent sequences: A324027 A324028 A324029 * A324031 A324032 A324033

Keyword

nonn,base

Author

Jianing Song, Sep 07 2019

Status

approved