A309450 The successive approximations up to 7^n for 7-adic integer 2^(1/5).

0, 4, 46, 95, 1124, 15530, 82758, 435705, 4553420, 27612624, 269734266, 1682110511, 9591417483, 9591417483, 9591417483, 4078929854577, 23069175894349, 122767967603152, 1053290023551980, 9195358013104225, 77588729125343083, 237173261720567085, 1354264989887135099

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..1182

Formula

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

Example

a(1) = (   4)_7 = 4,
a(2) = (  64)_7 = 46,
a(3) = ( 164)_7 = 95,
a(4) = (3164)_7 = 1124.

Maple

A:= op([1, 3], padic:-rootp(x^5 -2,  7, 25)):
seq(add(A[i]*10^(i-1), i=1..n), n=0..25); # Robert Israel, Aug 04 2019

Prog

(PARI) {a(n) = truncate((2+O(7^n))^(1/5))}

Crossrefs

Cf. A309445.

Expansions of p-adic integers:

A290567 (5-adic, 2^(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));

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

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

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

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

Sequence in context: A119729 A134110 A176312 * A119046 A273776 A131540

Adjacent sequences: A309447 A309448 A309449 * A309451 A309452 A309453

Keyword

nonn

Author

Seiichi Manyama, Aug 03 2019

Status

approved