OFFSET
0,2
COMMENTS
For n > 0, a(n) is the unique solution to x^2 == 3 (mod 13^n) in the range [0, 13^n - 1] and congruent to 9 modulo 13.
A322085 is the approximation (congruent to 4 mod 13) of another square root of 3 over the 13-adic field.
LINKS
Robert Israel, Table of n, a(n) for n = 0..896
Wikipedia, p-adic number
FORMULA
EXAMPLE
9^2 = 81 = 6*13 + 3.
61^2 = 3721 = 22*13^2 + 3.
1075^2 = 1155625 = 526*13^3 + 3.
MAPLE
S:= map(t -> op([1, 3], t), [padic:-evalp(RootOf(x^2-3, x), 13, 30)]):
S9:= op(select(t -> t[1]=9, S)):
seq(add(S9[i]*13^(i-1), i=1..n-1), n=1..31); # Robert Israel, Jun 13 2019
PROG
(PARI) a(n) = truncate(-sqrt(3+O(13^n)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Nov 26 2018
STATUS
approved