

A325489


Digits of one of the four 5adic 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 Anumber represents a 5adic number. The other square root is A325492.
For k not divisible by 5, k is a fourth power in 5adic field if and only if k == 1 (mod 5). If k is a fourth power in 5adic field, then k has exactly 4 fourthpower roots.


LINKS

Table of n, a(n) for n=0..87.
Wikipedia, padic 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 padic fourthpower roots:
this sequence, A325490, A325491, A325492 (5adic, 6^(1/4));
A324085, A324086, A324087, A324153 (13adic, 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



