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A325489 Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 1 mod 5. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A094884 A281540 A053216 * A278516 A292434 A138522

Adjacent sequences:  A325486 A325487 A325488 * A325490 A325491 A325492

KEYWORD

nonn,base

AUTHOR

Jianing Song, Sep 07 2019

STATUS

approved

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Last modified February 25 14:07 EST 2021. Contains 341609 sequences. (Running on oeis4.)