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A318962 Digits of one of the two 2-adic integers sqrt(-7) that ends in 01. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Over 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+1) is divisible by 2^(n+2), otherwise 1.

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

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

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

Sequence in context: A155031 A155029 A134540 * A128430 A176330 A266246

Adjacent sequences:  A318959 A318960 A318961 * A318963 A318964 A318965

KEYWORD

nonn,base

AUTHOR

Jianing Song, Sep 06 2018

STATUS

approved

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Last modified May 19 16:42 EDT 2019. Contains 323395 sequences. (Running on oeis4.)