A322565 Digits of one of the two 17-adic integers sqrt(-2) that is related to A322563.

7, 1, 12, 0, 9, 0, 16, 8, 5, 16, 14, 0, 1, 15, 11, 16, 15, 8, 13, 15, 11, 5, 11, 3, 9, 16, 16, 15, 3, 3, 0, 15, 7, 15, 16, 3, 14, 9, 12, 5, 2, 2, 4, 12, 12, 11, 11, 0, 9, 15, 12, 2, 9, 14, 2, 10, 6, 0, 8, 5, 15, 6, 6, 14, 9, 2, 10, 1, 7, 2, 13, 12, 3, 13, 6, 16

Offset

0,1

Comments

This square root of -2 in the 17-adic field ends with digit 7. The other, A322566, ends with digit 10 (A when written as a 17-adic number).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Wikipedia, p-adic number

Formula

a(n) = (A322563(n+1) - A322563(n))/17^n.

For n > 0, a(n) = 16 - A322566(n).

Equals A309989*A322561 = A309990*A322562.

Example

The solution to x^2 == -2 (mod 17^4) such that x == 7 (mod 17) is x == 3492 (mod 17^4), and 3492 is written as C17 in heptadecimal, so the first four terms are 7, 1, 12 and 0.

Prog

(PARI) a(n) = truncate(sqrt(-2+O(17^(n+1))))\17^n

Crossrefs

Cf. A322563, A322564.

Digits of 17-adic square roots:

A309989, A309990 (sqrt(-1));

A322561, A322562 (sqrt(2));

this sequence, A322566 (sqrt(-2)).

Sequence in context: A331337 A211836 A165949 * A343227 A339965 A364094

Adjacent sequences: A322562 A322563 A322564 * A322566 A322567 A322568

Keyword

nonn,base

Author

Jianing Song, Aug 29 2019

Status

approved