A321076 -id:A321076 - cp's OEIS frontend

A321078 Digits of one of the two 11-adic integers sqrt(5).

4, 4, 10, 4, 0, 9, 5, 8, 7, 7, 3, 9, 7, 4, 1, 8, 10, 5, 10, 8, 10, 2, 5, 6, 10, 10, 3, 10, 2, 2, 1, 6, 6, 5, 7, 10, 0, 6, 9, 8, 3, 1, 6, 5, 3, 1, 9, 0, 5, 8, 8, 10, 4, 8, 9, 1, 9, 7, 1, 2, 1, 0, 5, 0, 2, 9, 1, 5, 2, 1, 3, 1, 7, 10, 3, 5, 0, 4, 10, 5, 1, 2, 10, 2, 1, 3, 0

Offset: 0

Jianing Song, Oct 27 2018

This square root of 5 in the 11-adic field ends with digit 4. The other, A321079, ends with digit 7.

			...8960A7566122A3AA652A8A5A8147937785904A44.

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, p-adic number

Cf. A321076, A321079.

a(n) = truncate(sqrt(5+O(11^(n+1))))\11^n

a(n) = (A321076(n+1) - A321076(n))/11^n.

For n > 0, a(n) = 10 - A321079(n).

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).

Original entry on oeis.org

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

Offset: 0

Jianing Song, Oct 27 2018

nonn

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.

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

Wikipedia, p-adic number

Cf. A321076, A321079.

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

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

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

cp's OEIS Frontend

A321078 Digits of one of the two 11-adic integers sqrt(5).

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