A318962 Digits of one of the two 2-adic integers sqrt(-7) that ends in 01.

1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0,1

Comments

Over the 2-adic integers there are 2 solutions to x^2 = -7, one ends in 01 and the other ends in 11. This sequence gives the former one. See A318960 for detailed information.

Links

Jianing Song, Table of n, a(n) for n = 0..1000

Formula

a(0) = 1, a(1) = 0; for n >= 2, a(n) = 0 if A318960(n)^2 + 7 is divisible by 2^(n+2), otherwise 1.

a(n) = 1 - A318963(n) for n >= 1.

For n >= 2, a(n) = (A318960(n+1) - A318960(n))/2^n.

Example

...10110001110011100100110001100000010110101.

Prog

(PARI) a(n) = truncate(-sqrt(-7+O(2^(n+2))))\2^n

Crossrefs

Cf. A318960.

Digits of p-adic integers:

this sequence, A318963 (2-adic, sqrt(-7));

A271223, A271224 (3-adic, sqrt(-2));

A269591, A269592 (5-adic, sqrt(-4));

A210850, A210851 (5-adic, sqrt(-1));

A290566 (5-adic, 2^(1/3));

A290563 (5-adic, 3^(1/3));

A290794, A290795 (7-adic, sqrt(-6));

A290798, A290799 (7-adic, sqrt(-5));

A290796, A290797 (7-adic, sqrt(-3));

A212152, A212155 (7-adic, (1+sqrt(-3))/2);

A051277, A290558 (7-adic, sqrt(2));

A286838, A286839 (13-adic, sqrt(-1));

A309989, A309990 (17-adic, sqrt(-1)).

Also there are numerous sequences related to digits of 10-adic integers.

Sequence in context: A155029 A155031 A134540 * A128430 A176330 A363914

Adjacent sequences: A318959 A318960 A318961 * A318963 A318964 A318965

Keyword

nonn,base

Author

Jianing Song, Sep 06 2018

Extensions

Corrected by Jianing Song, Aug 28 2019

Status

approved