A319739 The 10-adic integer cube root of one seventh (1/7), that is, satisfying 7 * x^3 == 1 (mod 10^(n+1)), for all n.

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

Offset: 0

Author

Patrick A. Thomas, Sep 26 2018

Keywords

• nonn
• base
• easy

Examples

			25380616954407^3 * 7 == 1 (mod 10^14).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Digits of 10-adic integers:

A225405 ( 7^(1/3));

A225411 ( (1/3)^(1/3));

A225412 ( (1/9)^(1/3));

A225451 ( (1/3)^(1/7));

this sequence ( (1/7)^(1/3));

A319740 ((1/11)^(1/3)).

Programs

PARI

seq(n)={my(v=vector(n), t=0, b=1); for(i=1, #v, for(q=0, 9, if(lift(7*Mod(t, 10*b)^3)==1, v[i]=q; break); t+=b); b*=10); v} \\ Andrew Howroyd, Nov 26 2018

PARI

seq(n)={Vecrev(digits(lift(chinese( Mod((1/7 + O(5^n))^(1/3), 5^n), Mod((1/7 + O(2^n))^(1/3), 2^n)))), n)} \\ Andrew Howroyd, Nov 26 2018

Extensions

a(55)-a(89) from Andrew Howroyd, Nov 26 2018

a(90)-a(199) from Patrick A. Thomas, Jan 13 2019

Offset changed to 0 by Seiichi Manyama, Aug 17 2019