A325492 Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 4 mod 5.

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

Offset

0,1

Comments

One of the two square roots of A324025, where an A-number represents a 5-adic number. The other square root is A325489.

For k not divisible by 5, k is a fourth power in 5-adic field if and only if k == 1 (mod 5). If k is a fourth power in 5-adic field, then k has exactly 4 fourth-power roots.

Links

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

Wikipedia, p-adic number

Formula

Equals A325490*A210850 = A325491*A210851.

a(n) = (A325487(n+1) - A325487(n))/5^n.

For n > 0, a(n) = 4 - A325489(n).

Example

The unique number k in [1, 5^3] and congruent to 4 modulo 5 such that k^4 - 6 is divisible by 5^3 is k = 4 = (4)_5, so the first three terms are 4, 0 and 0.

Prog

(PARI) a(n) = lift(-sqrtn(6+O(5^(n+1)), 4))\5^n

Crossrefs

Cf. A210850, A210851, A324025, A325484, A325485, A325486, A325487.

Digits of p-adic fourth-power roots:

A325489, A325490, A325491, this sequence (5-adic, 6^(1/4));

A324085, A324086, A324087, A324153 (13-adic, 3^(1/4)).

Sequence in context: A193717 A020808 A198364 * A266270 A091467 A224861

Adjacent sequences: A325489 A325490 A325491 * A325493 A325494 A325495

Keyword

nonn,base

Author

Jianing Song, Sep 07 2019

Status

approved