

A324153


Digits of one of the four 13adic integers 3^(1/4) that is congruent to 11 mod 13.


12



11, 10, 5, 11, 0, 6, 0, 8, 4, 6, 11, 2, 8, 6, 5, 4, 2, 11, 0, 3, 3, 5, 12, 0, 9, 6, 8, 7, 1, 0, 9, 1, 3, 7, 4, 8, 8, 10, 5, 8, 1, 4, 8, 2, 11, 12, 10, 11, 8, 9, 1, 5, 9, 6, 9, 10, 6, 5, 9, 6, 11, 12, 9, 12, 1, 4, 1, 6, 1, 12, 9, 7, 8, 5, 3, 2, 0, 6, 1, 7, 11
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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 A324085.
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

Robert Israel, Table of n, a(n) for n = 0..10000
Wikipedia, padic number


FORMULA

Equals A324086*A286839 = A324087*A286838.
a(n) = (A324084(n+1)  A324084(n))/13^n.
For n > 0, a(n) = 12  A324085(n).


EXAMPLE

The unique number k in [1, 13^3] and congruent to 11 modulo 13 such that k^4  3 is divisible by 13^3 is k = 986 = (5AB)_13, so the first three terms are 11, 10 and 5.


MAPLE

R:= select(t > op([1, 3, 1], t)=11, [padic:rootp(x^43, 13, 101)]):
op([1, 1, 3], R); # Robert Israel, Sep 08 2019


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, A324085, A324086, A324087.
Sequence in context: A256078 A078200 A105034 * A065001 A022967 A023453
Adjacent sequences: A324150 A324151 A324152 * A324154 A324155 A324156


KEYWORD

nonn,base


AUTHOR

Jianing Song, Sep 01 2019


STATUS

approved



