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

Author

Jianing Song, Sep 06 2018

Keywords

• nonn
• base

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.

Examples

			...10110001110011100100110001100000010110101.
		

Links

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

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.

Programs

PARI

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

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.

Extensions

Corrected by Jianing Song, Aug 28 2019