cp's OEIS Frontend

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.

%I A319739 #38 Aug 17 2019 08:57:30
%S A319739 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,
%T A319739 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,
%U A319739 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
%N 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.
%H A319739 Seiichi Manyama, <a href="/A319739/b319739.txt">Table of n, a(n) for n = 0..10000</a>
%e A319739 25380616954407^3 * 7 == 1 (mod 10^14).
%o A319739 (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
%o A319739 (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
%Y A319739 Digits of 10-adic integers:
%Y A319739 A225405       (     7^(1/3));
%Y A319739 A225411       ( (1/3)^(1/3));
%Y A319739 A225412       ( (1/9)^(1/3));
%Y A319739 A225451       ( (1/3)^(1/7));
%Y A319739 this sequence ( (1/7)^(1/3));
%Y A319739 A319740       ((1/11)^(1/3)).
%K A319739 nonn,base,easy
%O A319739 0,1
%A A319739 _Patrick A. Thomas_, Sep 26 2018
%E A319739 a(55)-a(89) from _Andrew Howroyd_, Nov 26 2018
%E A319739 a(90)-a(199) from _Patrick A. Thomas_, Jan 13 2019
%E A319739 Offset changed to 0 by _Seiichi Manyama_, Aug 17 2019