

A309989


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


8



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

0,1


COMMENTS

This square root of 1 in the 17adic field ends with digit 4. The other, A309990, ends with digit 13 (D when written as a 17adic number).


LINKS

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


FORMULA

a(n) = (A286877(n+1)  A286877(n))/17^n.
For n > 0, a(n) = 16  A309990(n).


EXAMPLE

The solution to x^2 == 1 (mod 17^4) such that x == 4 (mod 17) is x == 27493 (mod 17^4), and 27493 is written as 5A24 in heptadecimal, so the first four terms are 4, 2, 10 and 5.


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));
this sequence, A309990 (17adic, sqrt(1)).
Sequence in context: A138569 A191725 A198326 * A283938 A283943 A283942
Adjacent sequences: A309986 A309987 A309988 * A309990 A309991 A309992


KEYWORD

nonn,base


AUTHOR

Jianing Song, Aug 26 2019


STATUS

approved



