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

Author

Jianing Song, Oct 27 2018

Keywords

• nonn
• base
• easy

Comments

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

Examples

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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. A321072, A321075, A322087, A322088.

Programs

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

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