A322566 Digits of one of the two 17-adic integers sqrt(-2) that is related to A322564.

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

Offset

0,1

Comments

This square root of -2 in the 17-adic field ends with digit 10 (A when written as a 17-adic number). The other, A322565, ends with digit 7.

Links

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

Wikipedia, p-adic number

Formula

a(n) = (A322564(n+1) - A322564(n))/17^n.

For n > 0, a(n) = 16 - A322565(n).

Equals A309989*A322562 = A309990*A322561.

Example

The solution to x^2 == -2 (mod 17^4) such that x == 10 (mod 17) is x == 80029 (mod 17^4), and 80029 is written as G4FA in heptadecimal, so the first four terms are 10, 15, 4 and 16.

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));

A322565, this sequence (sqrt(-2)).

Sequence in context: A167334 A236145 A246769 * A004475 A216118 A329772

Adjacent sequences: A322563 A322564 A322565 * A322567 A322568 A322569

Keyword

nonn,base

Author

Jianing Song, Aug 29 2019

Status

approved