

A324087


Digits of one of the four 3adic integers 3^(1/4) that is congruent to 10 mod 13.


11



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

0,1


COMMENTS

One of the two square roots of A322088, where an Anumber represents a 13adic number. The other square root is A324086.
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 A324085*A286838 = A324153*A286839.
a(n) = (A324083(n+1)  A324083(n))/13^n.
For n > 0, a(n) = 12  A324086(n).


EXAMPLE

The unique number k in [1, 13^3] and congruent to 10 modulo 13 such that k^4  3 is divisible by 13^3 is k = 1622 = (97A)_13, so the first three terms are 10, 7 and 9.


PROG

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


CROSSREFS

Cf. A286838, A286839, A322087, A324077, A324082, A324083, A324084, A324085, A324086, A324153.
Sequence in context: A089245 A098592 A016731 * A068444 A210285 A190996
Adjacent sequences: A324084 A324085 A324086 * A324088 A324089 A324090


KEYWORD

nonn,base


AUTHOR

Jianing Song, Sep 01 2019


STATUS

approved



