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

Author

Jianing Song, Nov 26 2018

Keywords

• nonn
• base
• easy

Comments

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

Examples

			...10B47929C097954C47A7C773116286B233BA04649.
		

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

Crossrefs

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

Programs

PARI

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

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