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A321107
Digits of one of the three 13-adic integers 5^(1/3) that is related to A320915.
13
8, 0, 1, 5, 7, 0, 5, 12, 8, 10, 11, 6, 9, 3, 4, 5, 8, 1, 5, 3, 0, 7, 1, 2, 7, 8, 8, 3, 4, 1, 0, 11, 4, 0, 0, 5, 4, 7, 2, 9, 4, 3, 4, 11, 11, 6, 8, 12, 11, 5, 2, 1, 7, 12, 7, 7, 11, 11, 0, 6, 5, 9, 6, 12, 5, 3, 11, 5, 12, 4, 9, 5, 1, 9, 9, 3, 8, 0, 7, 0, 3
OFFSET
0,1
COMMENTS
For k not divisible by 5, k is a cube in 13-adic field if and only if k == 1, 5, 8, 12 (mod 13). If k is a cube in 13-adic field, then k has exactly three cubic roots.
LINKS
Wikipedia, p-adic number
FORMULA
a(n) = (A320915(n+1) - A320915(n))/13^n.
EXAMPLE
The unique number k in [1, 13^3] and congruent to 8 modulo 13 such that k^3 - 5 is divisible by 13^3 is k = 177 = (108)_13, so the first three terms are 8, 0 and 1.
PROG
(PARI) a(n) = lift(sqrtn(5+O(13^(n+1)), 3))\13^n
CROSSREFS
For 5-adic cubic roots, see A290566, A290563, A309443.
Sequence in context: A011470 A345295 A198940 * A198117 A241215 A272343
KEYWORD
nonn,base
AUTHOR
Jianing Song, Aug 27 2019
STATUS
approved