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A309452 The successive approximations up to 7^n for 7-adic integer 4^(1/5).

%I A309452 #11 Aug 03 2019 14:19:28
%S A309452 0,2,9,107,450,450,67678,655923,2303009,13832611,54186218,1749037712,
%T A309452 13612998170,27454285371,124343295778,4193681732872,18436366262701,
%U A309452 217833949680307,1380986519616342,3009400117526791,3009400117526791,162593932712750793,3513869117212454835
%N A309452 The successive approximations up to 7^n for 7-adic integer 4^(1/5).
%F A309452 a(0) = 0 and a(1) = 2, a(n) = a(n-1) + 2 * (a(n-1)^5 - 4) mod 7^n for n > 1.
%e A309452 a(1) = (   2)_7 = 2,
%e A309452 a(2) = (  12)_7 = 9,
%e A309452 a(3) = ( 212)_7 = 107,
%e A309452 a(4) = (1212)_7 = 450.
%o A309452 (PARI) {a(n) = truncate((4+O(7^n))^(1/5))}
%Y A309452 Cf. A309447.
%Y A309452 Expansions of p-adic integers:
%Y A309452 A290800, A290802 (7-adic, sqrt(-6));
%Y A309452 A290806, A290809 (7-adic, sqrt(-5));
%Y A309452 A290803, A290804 (7-adic, sqrt(-3));
%Y A309452 A210852, A212153 (7-adic, (1+sqrt(-3))/2);
%Y A309452 A290557, A290559 (7-adic, sqrt(2));
%Y A309452 A309450 (7-adic, 2^(1/5));
%Y A309452 A309451 (7-adic, 3^(1/5));
%Y A309452 A309453 (7-adic, 5^(1/5));
%Y A309452 A309454 (7-adic, 6^(1/5)).
%K A309452 nonn
%O A309452 0,2
%A A309452 _Seiichi Manyama_, Aug 03 2019