A324024 One of the two successive approximations up to 5^n for 5-adic integer sqrt(6). This is the 4 (mod 5) case (except for n = 0).

0, 4, 9, 109, 109, 1359, 10734, 41984, 120109, 1291984, 3245109, 13010734, 208323234, 452463859, 1673166984, 13880198234, 44397776359, 349573557609, 1875452463859, 9504846995109, 9504846995109, 104872278635734, 581709436838859, 7734266809885734, 7734266809885734

Offset

0,2

Comments

For n > 0, a(n) is the unique solution to x^2 == 6 (mod 5^n) in the range [0, 5^n - 1] and congruent to 1 modulo 5.

A324023 is the approximation (congruent to 4 mod 5) of another square root of 6 over the 5-adic field.

Links

Table of n, a(n) for n=0..24.

Wikipedia, p-adic number

Formula

For n > 0, a(n) = 5^n - A324023(n).

a(n) = A048898(n)*A324027(n) mod 5^n = A048899(n)*A324028(n) mod 5^n.

Example

9^2 = 81 = 3*5^2 + 6;
109^2 = 11881 = 95*5^3 + 6 = 19*5^4 + 6;
1359^2 = 1846881 = 591*5^5 + 6.

Prog

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

Crossrefs

Cf. A048898, A048899, A324025, A324026.

Approximations of 5-adic square roots:

A324027, A324028 (sqrt(-6));

A268922, A269590 (sqrt(-4));

A048898, A048899 (sqrt(-1));

A324023, this sequence (sqrt(6)).

Sequence in context: A061272 A117680 A042649 * A042381 A230743 A367075

Adjacent sequences: A324021 A324022 A324023 * A324025 A324026 A324027

Keyword

nonn

Author

Jianing Song, Sep 07 2019

Status

approved