|
| |
|
|
A318962
|
|
Digits of one of the two 2-adic integers sqrt(-7) that ends in 01.
|
|
9
|
|
|
|
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 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 A266246
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
|
| |
|
|
