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A309450 The successive approximations up to 7^n for 7-adic integer 2^(1/5).

%I A309450 #11 Aug 04 2019 14:56:20
%S A309450 0,4,46,95,1124,15530,82758,435705,4553420,27612624,269734266,
%T A309450 1682110511,9591417483,9591417483,9591417483,4078929854577,
%U A309450 23069175894349,122767967603152,1053290023551980,9195358013104225,77588729125343083,237173261720567085,1354264989887135099
%N A309450 The successive approximations up to 7^n for 7-adic integer 2^(1/5).
%H A309450 Robert Israel, <a href="/A309450/b309450.txt">Table of n, a(n) for n = 0..1182</a>
%F A309450 a(0) = 0 and a(1) = 4, a(n) = a(n-1) + (a(n-1)^5 - 2) mod 7^n for n > 1.
%e A309450 a(1) = (   4)_7 = 4,
%e A309450 a(2) = (  64)_7 = 46,
%e A309450 a(3) = ( 164)_7 = 95,
%e A309450 a(4) = (3164)_7 = 1124.
%p A309450 A:= op([1,3],padic:-rootp(x^5 -2,  7, 25)):
%p A309450 seq(add(A[i]*10^(i-1),i=1..n),n=0..25); # _Robert Israel_, Aug 04 2019
%o A309450 (PARI) {a(n) = truncate((2+O(7^n))^(1/5))}
%Y A309450 Cf. A309445.
%Y A309450 Expansions of p-adic integers:
%Y A309450 A290567 (5-adic, 2^(1/3));
%Y A309450 A290800, A290802 (7-adic, sqrt(-6));
%Y A309450 A290806, A290809 (7-adic, sqrt(-5));
%Y A309450 A290803, A290804 (7-adic, sqrt(-3));
%Y A309450 A210852, A212153 (7-adic, (1+sqrt(-3))/2);
%Y A309450 A290557, A290559 (7-adic, sqrt(2));
%Y A309450 A309451 (7-adic, 3^(1/5));
%Y A309450 A309452 (7-adic, 4^(1/5));
%Y A309450 A309453 (7-adic, 5^(1/5));
%Y A309450 A309454 (7-adic, 6^(1/5)).
%K A309450 nonn
%O A309450 0,2
%A A309450 _Seiichi Manyama_, Aug 03 2019