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A322086

One of the two successive approximations up to 13^n for 13-adic integer sqrt(3). Here the 9 (mod 13) case (except for n = 0).

0, 9, 61, 1075, 9863, 9863, 3722793, 56817692, 245063243, 2692255406, 23901254152, 1540344664491, 12293307028713, 198677988008561, 804428201193067, 24428686515388801, 75614579529479558, 741031188712659399, 26692278946856673198, 813880127610558425101, 11047322160238681199840

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OFFSET

0,2

COMMENTS

For n > 0, a(n) is the unique solution to x^2 == 3 (mod 13^n) in the range [0, 13^n - 1] and congruent to 9 modulo 13.

A322085 is the approximation (congruent to 4 mod 13) of another square root of 3 over the 13-adic field.

LINKS

Robert Israel, Table of n, a(n) for n = 0..896

Wikipedia, p-adic number

FORMULA

For n > 0, a(n) = 13^n - A322085(n).

a(n) = Sum_{i=0..n-1} A322088(i)*13^i.