A321075 Digits of one of the two 11-adic integers sqrt(3).

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

Offset

0,1

Comments

This square root of 3 in the 11-adic field ends with digit 6. The other, A321074, ends with digit 5.

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) = (A321073(n+1) - A321073(n))/11^n.

For n > 0, a(n) = 10 - A321074(n).

This 11-adic integer equals the 11-adic limit as n -> oo of 2*T(11^n,3), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Dec 05 2022

Example

...1A174253A71419621A55A7719167281761192486.

Prog

(PARI) a(n) = truncate(-sqrt(3+O(11^(n+1))))\11^n

Crossrefs

Cf. A321073, A321074.

Sequence in context: A350795 A352769 A335005 * A234846 A371467 A244054

Adjacent sequences: A321072 A321073 A321074 * A321076 A321077 A321078

Keyword

nonn,base,easy

Author

Jianing Song, Oct 27 2018

Status

approved