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

0,1

Links

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

Example

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

Prog

(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

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)).

Sequence in context: A201424 A070513 A065463 * A242780 A324997 A011392

Adjacent sequences: A319736 A319737 A319738 * A319740 A319741 A319742

Keyword

nonn,base,easy

Author

Patrick A. Thomas, Sep 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

Status

approved