

A324085


Digits of one of the four 3adic integers 3^(1/4) that is congruent to 2 mod 13.


13



2, 2, 7, 1, 12, 6, 12, 4, 8, 6, 1, 10, 4, 6, 7, 8, 10, 1, 12, 9, 9, 7, 0, 12, 3, 6, 4, 5, 11, 12, 3, 11, 9, 5, 8, 4, 4, 2, 7, 4, 11, 8, 4, 10, 1, 0, 2, 1, 4, 3, 11, 7, 3, 6, 3, 2, 6, 7, 3, 6, 1, 0, 3, 0, 11, 8, 11, 6, 11, 0, 3, 5, 4, 7, 9, 10, 12, 6, 11, 5, 1
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OFFSET

0,1


COMMENTS

One of the two square roots of A322087, where an Anumber represents a 13adic number. The other square root is A324153.
For k not divisible by 13, k is a fourth power in 13adic field if and only if k == 1, 3, 9 (mod 13). If k is a fourth power in 13adic field, then k has exactly 4 fourthpower roots.


LINKS

Table of n, a(n) for n=0..80.
Wikipedia, padic number


FORMULA

Equals A324086*A286838 = A324087*A286839.
a(n) = (A324077(n+1)  A324077(n))/13^n.
For n > 0, a(n) = 12  A324153(n).


EXAMPLE

The unique number k in [1, 13^3] and congruent to 2 modulo 13 such that k^4  3 is divisible by 13^3 is k = 1211 = (722)_13, so the first three terms are 2, 7 and 7.


PROG

(PARI) a(n) = lift(sqrtn(3+O(13^(n+1)), 4) * sqrt(1+O(13^(n+1))))\13^n


CROSSREFS

Cf. A286838, A286839, A322087, A324077, A324082, A324083, A324084, A324086, A324087, A324153.
Sequence in context: A190256 A013671 A019807 * A340180 A063706 A110779
Adjacent sequences: A324082 A324083 A324084 * A324086 A324087 A324088


KEYWORD

nonn,base


AUTHOR

Jianing Song, Sep 01 2019


STATUS

approved



