OFFSET
0,1
COMMENTS
One of the two square roots of A322087, where an A-number represents a 13-adic number. The other square root is A324085.
For k not divisible by 13, k is a fourth power in 13-adic field if and only if k == 1, 3, 9 (mod 13). If k is a fourth power in 13-adic field, then k has exactly 4 fourth-power roots.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
Wikipedia, p-adic number
FORMULA
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^4-3, 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
KEYWORD
nonn,base
AUTHOR
Jianing Song, Sep 01 2019
STATUS
approved