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

0, 2, 9, 107, 450, 450, 67678, 655923, 2303009, 13832611, 54186218, 1749037712, 13612998170, 27454285371, 124343295778, 4193681732872, 18436366262701, 217833949680307, 1380986519616342, 3009400117526791, 3009400117526791, 162593932712750793, 3513869117212454835

Offset: 0

Author

Seiichi Manyama, Aug 03 2019

Keywords

• nonn

Examples

			a(1) = (   2)_7 = 2,
a(2) = (  12)_7 = 9,
a(3) = ( 212)_7 = 107,
a(4) = (1212)_7 = 450.
		

Crossrefs

Cf. A309447.

Expansions of p-adic integers:

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));

A309451 (7-adic, 3^(1/5));

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

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

Programs

PARI

{a(n) = truncate((4+O(7^n))^(1/5))}

Formula

a(0) = 0 and a(1) = 2, a(n) = a(n-1) + 2 * (a(n-1)^5 - 4) mod 7^n for n > 1.