A321074 Digits of one of the two 11-adic integers sqrt(3).

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

Offset

0,1

Comments

This square root of 3 in the 11-adic field ends with digit 5. The other, A321075, ends with digit 6.

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) = (A321072(n+1) - A321072(n))/11^n.

For n > 0, a(n) = 10 - A321075(n).

This 11-adic integer equals the 11-adic limit as n -> oo of 2*T(11^n,5/2), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Dec 05 2022

Example

...9093685703969148905503391943829349918625.

Prog

(PARI) a(n) = truncate(sqrt(3+O(11^(n+1))))\11^n
(PARI) seq(n)={Vecrev(digits(truncate(sqrt(3 + O(11^n))), 11), n)} \\ Andrew Howroyd, Nov 03 2018

Crossrefs

Cf. A321072, A321075, A322087, A322088.

Sequence in context: A054400 A035568 A344964 * A318384 A091660 A307029

Adjacent sequences: A321071 A321072 A321073 * A321075 A321076 A321077

Keyword

nonn,base,easy

Author

Jianing Song, Oct 27 2018

Status

approved