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A324153 Digits of one of the four 13-adic integers 3^(1/4) that is congruent to 11 mod 13. 14
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 (list; graph; refs; listen; history; text; internal format)
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
Wikipedia, p-adic number
FORMULA
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^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
Sequence in context: A256078 A078200 A105034 * A065001 A022967 A023453
KEYWORD
nonn,base
AUTHOR
Jianing Song, Sep 01 2019
STATUS
approved

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Last modified March 18 21:02 EDT 2024. Contains 370951 sequences. (Running on oeis4.)