A322169 Digits of the 5-adic integer 7^(1/5).

2, 4, 1, 3, 1, 4, 1, 4, 1, 0, 3, 2, 3, 3, 1, 1, 3, 1, 1, 3, 3, 3, 3, 1, 4, 1, 2, 4, 2, 0, 0, 1, 0, 0, 3, 0, 3, 2, 1, 3, 0, 0, 3, 2, 4, 1, 1, 0, 3, 3, 2, 2, 3, 0, 2, 0, 3, 3, 3, 1, 2, 0, 2, 0, 0, 0, 0, 3, 3, 0, 0, 2, 0, 3, 1, 1, 0, 4, 1, 0, 4, 0, 4, 0, 3, 4, 0, 3

Offset

0,1

Comments

For k not divisible by 5, k is a fifth power in 5-adic field if and only if k == 1, 7, 18, 24 (mod 25). If k is a fifth power in 5-adic field, then k has exactly one fifth root.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Wikipedia, p-adic number

Formula

a(n) = (A322157(n+1) - A322157(n))/5^n.

Example

The unique number k in [1, 5^5] such that k^5 - 7 is divisible by 5^6 is k = 1047 = (13142)_5, so the first five terms are 2, 4, 1, 3 and 1.

Maple

op([1, 3], padic:-rootp(x^5-7, 5, 100)); # Robert Israel, Aug 28 2019

Prog

(PARI) a(n) = lift(sqrtn(7+O(5^(n+2)), 5))\5^n

Crossrefs

Cf. A322157.

For fifth roots in 7-adic field, see A309445, A309446, A309447, A309448, A309449.

Sequence in context: A257164 A190555 A141843 * A332084 A130266 A261595

Adjacent sequences: A322166 A322167 A322168 * A322170 A322171 A322172

Keyword

nonn,base

Author

Jianing Song, Aug 28 2019

Status

approved