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A324029 Digits of one of the two 5-adic integers sqrt(-6) that is related to A324027. 7
2, 2, 1, 1, 2, 3, 2, 4, 3, 1, 0, 0, 1, 3, 1, 3, 4, 2, 3, 2, 3, 2, 4, 4, 2, 3, 3, 0, 1, 1, 3, 1, 1, 1, 3, 1, 2, 3, 2, 3, 4, 1, 0, 2, 4, 4, 3, 4, 0, 3, 2, 0, 2, 0, 2, 0, 3, 2, 0, 0, 4, 2, 4, 4, 0, 4, 4, 4, 3, 1, 4, 2, 2, 4, 2, 0, 0, 0, 3, 0, 4, 3, 2, 4, 3, 3, 4, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
This square root of -6 in the 5-adic field ends with digit 2. The other, A324030, ends with digit 3.
LINKS
Wikipedia, p-adic number
FORMULA
a(n) = (A324027(n+1) - A324027(n))/5^n.
For n > 0, a(n) = 4 - A324030(n).
Equals A210850*A324026 = A210851*A324025, where each A-number represents a 5-adic number.
EXAMPLE
The solution to x^2 == -6 (mod 5^4) such that x == 2 (mod 5) is x == 162 (mod 5^4), and 162 is written as 1122 in quinary, so the first four terms are 2, 2, 1 and 1.
PROG
(PARI) a(n) = truncate(sqrt(-6+O(5^(n+1))))\5^n
CROSSREFS
Digits of 5-adic square roots:
this sequence, A324030 (sqrt(-6));
A269591, A269592 (sqrt(-4));
A210850, A210851 (sqrt(-1));
A324025, A324026 (sqrt(6)).
Sequence in context: A339352 A305825 A366780 * A334046 A136605 A165621
KEYWORD
nonn,base
AUTHOR
Jianing Song, Sep 07 2019
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)