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A322562
Digits of one of the two 17-adic integers sqrt(2) that is related to A322560.
6
11, 2, 2, 8, 11, 12, 2, 2, 9, 14, 1, 1, 5, 11, 10, 9, 14, 2, 10, 2, 1, 0, 13, 8, 2, 11, 4, 0, 16, 12, 9, 16, 8, 6, 14, 0, 0, 1, 7, 9, 4, 7, 2, 2, 11, 4, 13, 12, 9, 7, 7, 14, 14, 2, 11, 7, 4, 10, 14, 6, 11, 16, 6, 6, 5, 5, 14, 13, 2, 6, 5, 14, 10, 4, 16, 12
OFFSET
0,1
COMMENTS
This square root of 2 in the 17-adic field ends with digit 11 (B when written as a 17-adic number). The other, A322561, ends with digit 6.
LINKS
Wikipedia, p-adic number
FORMULA
a(n) = (A322560(n+1) - A322560(n))/17^n.
For n > 0, a(n) = 16 - A322561(n).
EXAMPLE
The solution to x^2 == 2 (mod 17^4) such that x == 11 (mod 17) is x == 39927 (mod 17^4), and 39927 is written as 822B in heptadecimal, so the first four terms are 11, 2, 2 and 8.
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, this sequence (sqrt(2));
A322565, A322566 (sqrt(-2)).
Sequence in context: A323454 A261353 A087774 * A040118 A099268 A070277
KEYWORD
nonn,base
AUTHOR
Jianing Song, Aug 29 2019
STATUS
approved