A325489 Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 1 mod 5.

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

Offset

0,2

Comments

One of the two square roots of A324025, where an A-number represents a 5-adic number. The other square root is A325492.

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*A210851 = A325491*A210850.

a(n) = (A325484(n+1) - A325484(n))/5^n.

For n > 0, a(n) = 4 - A325492(n).

Example

The unique number k in [1, 5^3] and congruent to 1 modulo 5 such that k^4 - 6 is divisible by 5^3 is k = 121 = (441)_5, so the first three terms are 1, 4 and 4.

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:

this sequence, A325490, A325491, A325492 (5-adic, 6^(1/4));

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

Sequence in context: A359532 A281540 A053216 * A278516 A362329 A292434

Adjacent sequences: A325486 A325487 A325488 * A325490 A325491 A325492

Keyword

nonn,base

Author

Jianing Song, Sep 07 2019

Status

approved