A324026 Digits of one of the two 5-adic integers sqrt(6) that is related to A324024.

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

Offset

0,1

Comments

This square root of 6 in the 5-adic field ends with digit 4. The other, A324025, ends with digit 1.

Links

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

Wikipedia, p-adic number

Formula

a(n) = (A324024(n+1) - A324024(n))/5^n.

For n > 0, a(n) = 4 - A324025(n).

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

Example

The solution to x^2 == 6 (mod 5^4) such that x == 4 (mod 5) is x == 109 (mod 5^4), and 109 is written as 414 in quinary, so the first four terms are 4, 1, 4 and 0.

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));

A324025, this sequence (sqrt(6)).

Sequence in context: A298568 A152890 A143354 * A171539 A106141 A082999

Adjacent sequences: A324023 A324024 A324025 * A324027 A324028 A324029

Keyword

nonn,base

Author

Jianing Song, Sep 07 2019

Status

approved