A321076 One of the two successive approximations up to 11^n for 11-adic integer sqrt(5). Here the 4 (mod 11) case (except for n = 0).

0, 4, 48, 1258, 6582, 6582, 1456041, 10313846, 166211214, 1666723381, 18172357218, 95984631021, 2663789666520, 24632788303567, 162723636879291, 542473470462532, 33960458825787740, 493457757461509350, 3020692899957978205, 58619866034880293015, 547892589622196663343

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 4 modulo 11.

A321077 is the approximation (congruent to 7 mod 11) of another square root of 5 over the 11-adic field.

Examples

			4^2 = 16 = 5 + 1*11.
48^2 = 2304 = 5 + 19*11^2.
1258^2 = 1582564 = 5 + 1189*11^3.
		

Links

• Wikipedia, p-adic number

Crossrefs

Cf. A321077, A321078.

Programs

PARI

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

Formula

For n > 0, a(n) = 11^n - A321077(n).

a(n) = Sum_{i=0..n-1} A321078(i)*11^i.