

A309990


Digits of one of the two 17adic integers sqrt(1).


8



13, 14, 6, 11, 4, 0, 4, 8, 3, 13, 2, 16, 10, 15, 16, 1, 15, 8, 2, 11, 9, 0, 2, 15, 11, 3, 7, 10, 11, 4, 0, 1, 7, 0, 2, 4, 0, 15, 13, 10, 12, 6, 1, 11, 0, 4, 14, 15, 11, 12, 16, 1, 14, 5, 2, 7, 11, 15, 5, 0, 1, 9, 11, 10, 2, 13, 4, 16, 16, 5, 4, 3, 7, 11, 12, 0
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OFFSET

0,1


COMMENTS

This square root of 1 in the 17adic field ends with digit 13 (D when written as a 17adic number). The other, A309989, ends with digit 4.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, padic number


FORMULA

a(n) = (A286878(n+1)  A286878(n))/17^n.
For n > 0, a(n) = 16  A309989(n).


EXAMPLE

The solution to x^2 == 1 (mod 17^4) such that x == 13 (mod 17) is x == 56028 (mod 17^4), and 56028 is written as B6ED in heptadecimal, so the first four terms are 13, 14, 6 and 11.


PROG

(PARI) a(n) = truncate(sqrt(1+O(17^(n+1))))\17^n


CROSSREFS

Cf. A286877, A286878.
Digits of padic square roots:
A318962, A318963 (2adic, sqrt(7));
A271223, A271224 (3adic, sqrt(2));
A269591, A269592 (5adic, sqrt(4));
A210850, A210851 (5adic, sqrt(1));
A290794, A290795 (7adic, sqrt(6));
A290798, A290799 (7adic, sqrt(5));
A290796, A290797 (7adic, sqrt(3));
A051277, A290558 (7adic, sqrt(2));
A321074, A321075 (11adic, sqrt(3));
A321078, A321079 (11adic, sqrt(5));
A322091, A322092 (13adic, sqrt(3));
A286838, A286839 (13adic, sqrt(1));
A322087, A322088 (13adic, sqrt(3));
A309989, this sequence (17adic, sqrt(1)).
Sequence in context: A094461 A186070 A254069 * A196461 A004502 A020512
Adjacent sequences: A309987 A309988 A309989 * A309991 A309992 A309993


KEYWORD

nonn,base


AUTHOR

Jianing Song, Aug 26 2019


STATUS

approved



