A309454 The successive approximations up to 7^n for 7-adic integer 6^(1/5).

0, 6, 20, 265, 1980, 11584, 11584, 246882, 1070425, 29894430, 29894430, 1159795426, 9069102398, 9069102398, 202847123212, 2237516341759, 2237516341759, 201635099759365, 1132157155708193, 6017397949439540, 17416293134812683, 496169890920484689, 1613261619087052703

Offset: 0

Author

Seiichi Manyama, Aug 03 2019

Keywords

• nonn

Examples

			a(1) = (   6)_7 = 6,
a(2) = (  26)_7 = 20,
a(3) = ( 526)_7 = 265,
a(4) = (5526)_7 = 1980.
		

Crossrefs

Cf. A309449.

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));

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

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

Programs

PARI

{a(n) = truncate((6+O(7^n))^(1/5))}

Formula

a(0) = 0 and a(1) = 6, a(n) = a(n-1) + 4 * (a(n-1)^5 - 6) mod 7^n for n > 1.