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

Author

Jianing Song, Sep 07 2019

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

• Wikipedia, p-adic number

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)).

Programs

PARI

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

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.