

A322169


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


6



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
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OFFSET

0,1


COMMENTS

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


LINKS

Robert Israel, Table of n, a(n) for n = 0..10000
Wikipedia, padic 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^57, 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 7adic 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



