A322088 Digits of one of the two 13-adic integers sqrt(3).

9, 4, 6, 4, 0, 10, 11, 3, 3, 2, 11, 6, 8, 2, 6, 1, 1, 3, 7, 7, 12, 7, 10, 7, 4, 12, 4, 5, 9, 7, 9, 0, 12, 9, 2, 9, 7, 4, 11, 0, 1, 4, 5, 12, 9, 11, 8, 3, 3, 3, 11, 2, 6, 0, 10, 5, 9, 7, 11, 6, 0, 11, 11, 0, 2, 7, 6, 1, 5, 4, 0, 2, 11, 9, 7, 7, 7, 5, 1, 11, 7

Offset

0,1

Comments

This square root of 3 in the 13-adic field ends with digit 9. The other, A322087, ends with digit 4.

Links

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

Peter Bala, Using Chebyshev polynomials to find the p-adic square roots of 2 and 3, Dec 2022.

Wikipedia, p-adic number

Formula

a(n) = (A322086(n+1) - A322086(n))/13^n.

For n > 0, a(n) = 12 - A322087(n).

Equals A286838*A322092 = A286839*A322091.

This 13-adic integer is the 13-adic limit as n -> oo of the integer sequence {2*T(13^n,9/2)}, where T(n,x) denotes the n-th Chebyshev polynomial. - Peter Bala, Dec 04 2022

Example

...10B47929C097954C47A7C773116286B233BA04649.

Prog

(PARI) a(n) = truncate(-sqrt(3+O(13^(n+1))))\13^n

Crossrefs

Cf. A286838, A286839, A322086, A322087, A322091, A322092.

Sequence in context: A289267 A197155 A153756 * A343199 A139720 A248177

Adjacent sequences: A322085 A322086 A322087 * A322089 A322090 A322091

Keyword

nonn,base,easy

Author

Jianing Song, Nov 26 2018

Status

approved