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A309453 The successive approximations up to 7^n for 7-adic integer 5^(1/5).

%I A309453 #11 Aug 03 2019 14:19:35
%S A309453 0,3,45,339,1368,8571,42185,630430,4748145,27807349,27807349,
%T A309453 1722658843,13586619301,41269193703,235047214517,2269716433064,
%U A309453 30755085492722,230152668910328,928044210871949,2556457808782398,36753143364901827,196337675960125829,2430521132293261857
%N A309453 The successive approximations up to 7^n for 7-adic integer 5^(1/5).
%F A309453 a(0) = 0 and a(1) = 3, a(n) = a(n-1) + (a(n-1)^5 - 5) mod 7^n for n > 1.
%e A309453 a(1) = (   3)_7 = 3,
%e A309453 a(2) = (  63)_7 = 45,
%e A309453 a(3) = ( 663)_7 = 339,
%e A309453 a(4) = (3663)_7 = 1368.
%o A309453 (PARI) {a(n) = truncate((5+O(7^n))^(1/5))}
%Y A309453 Cf. A309448.
%Y A309453 Expansions of p-adic integers:
%Y A309453 A290800, A290802 (7-adic, sqrt(-6));
%Y A309453 A290806, A290809 (7-adic, sqrt(-5));
%Y A309453 A290803, A290804 (7-adic, sqrt(-3));
%Y A309453 A210852, A212153 (7-adic, (1+sqrt(-3))/2);
%Y A309453 A290557, A290559 (7-adic, sqrt(2));
%Y A309453 A309450 (7-adic, 2^(1/5));
%Y A309453 A309451 (7-adic, 3^(1/5));
%Y A309453 A309452 (7-adic, 4^(1/5));
%Y A309453 A309454 (7-adic, 6^(1/5)).
%K A309453 nonn
%O A309453 0,2
%A A309453 _Seiichi Manyama_, Aug 03 2019