A319740 The 10-adic integer cube root of one eleventh (1/11), that is, satisfying 11 * x^3 == 1 (mod 10^n), for all n.

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

Offset: 1

Author

Patrick A. Thomas, Sep 26 2018

Keywords

• nonn
• base
• easy

Examples

			45016103979758167131^3 * 11 == 1 (mod 10^20).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A225402, A225411, A225412 (10-adic cube root of -1/3, 1/3, 1/9).

Programs

Maple

op([1,3], padic:-rootp(11*x^3-1,10,100)); # Robert Israel, Jan 03 2019

PARI

seq(n)={Vecrev(digits(lift(chinese( Mod((1/11 + O(5^n))^(1/3), 5^n), Mod((1/11 + O(2^n))^(1/3), 2^n)))), n)} \\ Andrew Howroyd, Nov 26 2018

Extensions

Terms a(56) and beyond from Andrew Howroyd, Nov 26 2018