A309444 The successive approximations up to 5^n for 5-adic integer 4^(1/3).

0, 4, 9, 59, 559, 3059, 12434, 59309, 371809, 371809, 8184309, 27715559, 76543684, 320684309, 1541387434, 25955449934, 86990606184, 392166387434, 2680984746809, 14125076543684, 52272049199934, 338374344121809, 2245722976934309, 7014094558965559, 42776881424199934

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(0) = 0 and a(1) = 4, a(n) = a(n-1) + 3 * (a(n-1)^3 - 4) mod 5^n for n > 1.

Example

a(1) = (   4)_5 = 4,
a(2) = (  14)_5 = 9,
a(3) = ( 214)_5 = 59,
a(4) = (4214)_5 = 559.

Prog

(PARI) {a(n) = truncate((4+O(5^n))^(1/3))}

Crossrefs

Cf. A309443.

Expansions of p-adic integers:

A268922, A269590 (5-adic, sqrt(-4));

A048898, A048899 (5-adic, sqrt(-1));

A290567 (5-adic, 2^(1/3));

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

Sequence in context: A109717 A197859 A197997 * A198178 A013571 A002942

Adjacent sequences: A309441 A309442 A309443 * A309445 A309446 A309447

Keyword

nonn

Author

Seiichi Manyama, Aug 03 2019

Status

approved