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A324024

One of the two successive approximations up to 5^n for 5-adic integer sqrt(6). This is the 4 (mod 5) case (except for n = 0).

0, 4, 9, 109, 109, 1359, 10734, 41984, 120109, 1291984, 3245109, 13010734, 208323234, 452463859, 1673166984, 13880198234, 44397776359, 349573557609, 1875452463859, 9504846995109, 9504846995109, 104872278635734, 581709436838859, 7734266809885734, 7734266809885734

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OFFSET

0,2

COMMENTS

For n > 0, a(n) is the unique solution to x^2 == 6 (mod 5^n) in the range [0, 5^n - 1] and congruent to 1 modulo 5.

A324023 is the approximation (congruent to 4 mod 5) of another square root of 6 over the 5-adic field.

LINKS

Table of n, a(n) for n=0..24.

Wikipedia, p-adic number

FORMULA

For n > 0, a(n) = 5^n - A324023(n).

a(n) = A048898(n)*A324027(n) mod 5^n = A048899(n)*A324028(n) mod 5^n.