A309451 The successive approximations up to 7^n for 7-adic integer 3^(1/5).

0, 5, 26, 75, 1104, 3505, 20312, 20312, 4961570, 28020774, 229788809, 512264058, 2489590801, 71696026806, 71696026806, 71696026806, 19061942066578, 218459525484184, 451090039471391

Offset: 0

Author

Seiichi Manyama, Aug 03 2019

Keywords

• nonn

Examples

			a(1) = (   5)_7 = 5,
a(2) = (  35)_7 = 26,
a(3) = ( 135)_7 = 75,
a(4) = (3135)_7 = 1104.
		

Crossrefs

Cf. A309446.

Expansions of p-adic integers:

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

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

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

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

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

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

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

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

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

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

Programs

PARI

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

Formula

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