

A321108


Digits of one of the three 13adic integers 5^(1/3) that is related to A321105.


13



11, 11, 5, 11, 2, 0, 9, 0, 6, 11, 9, 6, 7, 9, 2, 9, 9, 2, 3, 3, 8, 2, 7, 11, 6, 7, 4, 7, 10, 5, 5, 4, 11, 6, 2, 5, 2, 7, 10, 9, 9, 2, 9, 5, 7, 7, 4, 5, 10, 4, 1, 6, 4, 1, 4, 0, 4, 10, 11, 4, 12, 12, 7, 2, 9, 6, 11, 8, 5, 6, 11, 2, 0, 6, 6, 12, 10, 8, 12, 11, 2
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OFFSET

0,1


COMMENTS

For k not divisible by 5, k is a cube in 13adic field if and only if k == 1, 5, 8, 12 (mod 13). If k is a cube in 13adic field, then k has exactly three cubic roots.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, padic number


FORMULA

a(n) = (A321105(n+1)  A321105(n))/13^n.


EXAMPLE

The unique number k in [1, 13^3] and congruent to 11 modulo 13 such that k^3  5 is divisible by 13^3 is k = 999 = (5BB)_13, so the first three terms are 11, 11 and 5.


PROG

(PARI) a(n) = lift(sqrtn(5+O(13^(n+1)), 3) * (1sqrt(3+O(13^(n+1))))/2)\13^n


CROSSREFS

Cf. A320914, A320915, A321105, A321106, A321107.
For 5adic cubic roots, see A290566, A290563, A309443.
Sequence in context: A135684 A220295 A300289 * A126610 A087380 A152986
Adjacent sequences: A321105 A321106 A321107 * A321109 A321110 A321111


KEYWORD

nonn,base


AUTHOR

Jianing Song, Aug 27 2019


STATUS

approved



