

A319555


Digits of one of the three 7adic integers 6^(1/3) that is related to A319199.


10



6, 4, 1, 2, 1, 2, 0, 4, 4, 4, 1, 0, 6, 1, 0, 5, 2, 4, 4, 4, 2, 3, 1, 0, 6, 3, 1, 4, 2, 6, 1, 6, 1, 2, 1, 5, 4, 5, 5, 3, 4, 2, 6, 4, 0, 4, 3, 4, 4, 1, 0, 6, 5, 2, 4, 1, 4, 2, 2, 1, 5, 2, 4, 4, 2, 5, 4, 6, 5, 1, 0, 1, 6, 1, 1, 4, 0, 6, 3, 4, 4, 2, 3, 4, 0, 0, 4, 4
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OFFSET

0,1


COMMENTS

For k not divisible by 7, k is a cube in 7adic field if and only if k == 1, 6 (mod 13). If k is a cube in 7adic field, then k has exactly three cubic roots.


LINKS

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


FORMULA

Equals A319297*(A2121521) = A319297*A212152^2, where each Anumber represents a 7adic number.
Equals A319305*(A2121551) = A319305*A212155^2.


EXAMPLE

The unique number k in [1, 7^3] and congruent to 6 modulo 7 such that k^3  6 is divisible by 7^3 is k = 83 = (146)_7, so the first three terms are 6, 4 and 1.


PROG

(PARI) a(n) = lift(sqrtn(6+O(7^(n+1)), 3))\7^n


CROSSREFS

Cf. A319097, A319098, A319199.
Digits of padic cubic roots:
A290566 (5adic, 2^(1/3));
A290563 (5adic, 3^(1/3));
A309443 (5adic, 4^(1/3));
A319297, A319305, this sequence (7adic, 6^(1/3));
A321106, A321107, A321108 (13adic, 5^(1/3)).
Sequence in context: A106333 A104748 A117335 * A244980 A021863 A259620
Adjacent sequences: A319552 A319553 A319554 * A319556 A319557 A319558


KEYWORD

nonn,base


AUTHOR

Jianing Song, Aug 27 2019


STATUS

approved



