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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.
5
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
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
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