A321077 One of the two successive approximations up to 11^n for 11-adic integer sqrt(5). Here the 7 (mod 11) case (except for n = 0).

0, 7, 73, 73, 8059, 154469, 315520, 9173325, 48147667, 691224310, 7765067383, 189327039590, 474638710201, 9889923840364, 217026196703950, 3634774698953119, 11989271037784421, 11989271037784421, 2539224413534253276, 2539224413534253276, 124857405310363345858

Offset: 0

Author

Jianing Song, Oct 27 2018

Keywords

• nonn

Comments

For n > 0, a(n) is the unique solution to x^2 == 5 (mod 11^n) in the range [0, 11^n - 1] and congruent to 7 modulo 11.

A321076 is the approximation (congruent to 4 mod 11) of another square root of 5 over the 11-adic field.

Examples

			7^2 = 49 = 5 + 4*11.
73^2 = 5329 = 5 + 44*11^2 = 5 + 4*11^3.
		

Links

• Wikipedia, p-adic number

Crossrefs

Cf. A321076, A321079.

Programs

PARI

a(n) = truncate(-sqrt(5+O(11^n)))

Formula

For n > 0, a(n) = 11^n - A321076(n).

a(n) = Sum_{i=0..n-1} A321079(i)*11^i.