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A322087 Digits of one of the two 13-adic integers sqrt(3). 12
4, 8, 6, 8, 12, 2, 1, 9, 9, 10, 1, 6, 4, 10, 6, 11, 11, 9, 5, 5, 0, 5, 2, 5, 8, 0, 8, 7, 3, 5, 3, 12, 0, 3, 10, 3, 5, 8, 1, 12, 11, 8, 7, 0, 3, 1, 4, 9, 9, 9, 1, 10, 6, 12, 2, 7, 3, 5, 1, 6, 12, 1, 1, 12, 10, 5, 6, 11, 7, 8, 12, 10, 1, 3, 5, 5, 5, 7, 11, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
This square root of 3 in the 13-adic field ends with digit 4. The other, A322088, ends with digit 9.
LINKS
Wikipedia, p-adic number
FORMULA
a(n) = (A322085(n+1) - A322085(n))/13^n.
For n > 0, a(n) = 12 - A322088(n).
This 13-adic integer is the 13-adic limit as n -> oo of the integer sequence {2*T(13^n,2)}, where T(n,x) denotes the n-th Chebyshev polynomial. - Peter Bala, Dec 04 2022
EXAMPLE
...BC1853A30C35378085250559BB6A461A9912C8684.
PROG
(PARI) a(n) = truncate(sqrt(3+O(13^(n+1))))\13^n
CROSSREFS
Cf. A322085.
Digits of p-adic integers:
A321074, A321075 (11-adic, sqrt(3));
this sequence, A322088 (13-adic, sqrt(3));
A286838, A286839 (13-adic, sqrt(-1));
A322091, A322092 (13-adic, sqrt(-3)).
Sequence in context: A279160 A197290 A200368 * A142350 A011515 A005531
KEYWORD
nonn,base
AUTHOR
Jianing Song, Nov 26 2018
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)