A324025 Digits of one of the two 5-adic integers sqrt(6) that is related to A324023.

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

Offset

0,2

Comments

This square root of 6 in the 5-adic field ends with digit 1. The other, A324026, ends with digit 4.

Links

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

Wikipedia, p-adic number

Formula

a(n) = (A324023(n+1) - A324023(n))/5^n.

For n > 0, a(n) = 4 - A324026(n).

Equals A210850*A324030 = A210851*A324029, where each A-number represents a 5-adic number.

Example

The solution to x^2 == 6 (mod 5^4) such that x == 1 (mod 5) is x == 516 (mod 5^4), and 516 is written as 4031 in quinary, so the first four terms are 1, 3, 0 and 4.

Prog

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

Crossrefs

Cf. A324023, A324024.

Digits of 5-adic square roots:

A324029, A324030 (sqrt(-6));

A269591, A269592 (sqrt(-4));

A210850, A210851 (sqrt(-1));

this sequence, A324026 (sqrt(6)).

Sequence in context: A351190 A131486 A127445 * A081170 A201291 A272192

Adjacent sequences: A324022 A324023 A324024 * A324026 A324027 A324028

Keyword

nonn,base

Author

Jianing Song, Sep 07 2019

Status

approved