A309451 - OEIS

%I #10 Aug 03 2019 14:19:22

%S 0,5,26,75,1104,3505,20312,20312,4961570,28020774,229788809,512264058,

%T 2489590801,71696026806,71696026806,71696026806,19061942066578,

%U 218459525484184,451090039471391

%N The successive approximations up to 7^n for 7-adic integer 3^(1/5).

%F a(0) = 0 and a(1) = 5, a(n) = a(n-1) + 2 * (a(n-1)^5 - 3) mod 7^n for n > 1.

%e a(1) = (   5)_7 = 5,

%e a(2) = (  35)_7 = 26,

%e a(3) = ( 135)_7 = 75,

%e a(4) = (3135)_7 = 1104.

%o (PARI) {a(n) = truncate((3+O(7^n))^(1/5))}

%Y Cf. A309446.

%Y Expansions of p-adic integers:

%Y A290568 (5-adic, 3^(1/3));

%Y A290800, A290802 (7-adic, sqrt(-6));

%Y A290806, A290809 (7-adic, sqrt(-5));

%Y A290803, A290804 (7-adic, sqrt(-3));

%Y A210852, A212153 (7-adic, (1+sqrt(-3))/2);

%Y A290557, A290559 (7-adic, sqrt(2));

%Y A309450 (7-adic, 2^(1/5));

%Y A309452 (7-adic, 4^(1/5));

%Y A309453 (7-adic, 5^(1/5));

%Y A309454 (7-adic, 6^(1/5)).

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 03 2019