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A322565
Digits of one of the two 17-adic integers sqrt(-2) that is related to A322563.
6
7, 1, 12, 0, 9, 0, 16, 8, 5, 16, 14, 0, 1, 15, 11, 16, 15, 8, 13, 15, 11, 5, 11, 3, 9, 16, 16, 15, 3, 3, 0, 15, 7, 15, 16, 3, 14, 9, 12, 5, 2, 2, 4, 12, 12, 11, 11, 0, 9, 15, 12, 2, 9, 14, 2, 10, 6, 0, 8, 5, 15, 6, 6, 14, 9, 2, 10, 1, 7, 2, 13, 12, 3, 13, 6, 16
OFFSET
0,1
COMMENTS
This square root of -2 in the 17-adic field ends with digit 7. The other, A322566, ends with digit 10 (A when written as a 17-adic number).
LINKS
Wikipedia, p-adic number
FORMULA
a(n) = (A322563(n+1) - A322563(n))/17^n.
For n > 0, a(n) = 16 - A322566(n).
EXAMPLE
The solution to x^2 == -2 (mod 17^4) such that x == 7 (mod 17) is x == 3492 (mod 17^4), and 3492 is written as C17 in heptadecimal, so the first four terms are 7, 1, 12 and 0.
PROG
(PARI) a(n) = truncate(sqrt(-2+O(17^(n+1))))\17^n
CROSSREFS
Digits of 17-adic square roots:
A309989, A309990 (sqrt(-1));
A322561, A322562 (sqrt(2));
this sequence, A322566 (sqrt(-2)).
Sequence in context: A331337 A211836 A165949 * A343227 A339965 A364094
KEYWORD
nonn,base
AUTHOR
Jianing Song, Aug 29 2019
STATUS
approved