A318963 Digits of one of the two 2-adic integers sqrt(-7) that ends in 11.

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

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 latter one. See A318961 for detailed information.

Links

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

Formula

a(0) = a(1) = 1; for n >= 2, a(n) = 0 if A318961(n)^2 + 7 is divisible by 2^(n+2), otherwise 1.

a(n) = 1 - A318962(n) for n >= 1.

For n >= 2, a(n) = (A318961(n+1) - A318961(n))/2^n.

Example

...01001110001100011011001110011111101001011.

Prog

(PARI) a(n) = if(n==1, 1, truncate(sqrt(-7+O(2^(n+2))))\2^n)

Crossrefs

Cf. A318961.

Digits of p-adic integers:

A318962, this sequence (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: A068427 A190191 A189920 * A350600 A295896 A176918

Adjacent sequences: A318960 A318961 A318962 * A318964 A318965 A318966

Keyword

nonn,base

Author

Jianing Song, Sep 06 2018

Extensions

Corrected by Jianing Song, Aug 28 2019

Status

approved