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A322169
Digits of the 5-adic 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
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
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
KEYWORD
nonn,base
AUTHOR
Jianing Song, Aug 28 2019
STATUS
approved