A309453 The successive approximations up to 7^n for 7-adic integer 5^(1/5).

0, 3, 45, 339, 1368, 8571, 42185, 630430, 4748145, 27807349, 27807349, 1722658843, 13586619301, 41269193703, 235047214517, 2269716433064, 30755085492722, 230152668910328, 928044210871949, 2556457808782398, 36753143364901827, 196337675960125829, 2430521132293261857

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

Example

a(1) = (   3)_7 = 3,
a(2) = (  63)_7 = 45,
a(3) = ( 663)_7 = 339,
a(4) = (3663)_7 = 1368.

Prog

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

Crossrefs

Cf. A309448.

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));

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

Sequence in context: A370954 A117972 A061532 * A360716 A060242 A271236

Adjacent sequences: A309450 A309451 A309452 * A309454 A309455 A309456

Keyword

nonn

Author

Seiichi Manyama, Aug 03 2019

Status

approved