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A319555
Digits of one of the three 7-adic integers 6^(1/3) that is related to A319199.
12
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
OFFSET
0,1
COMMENTS
For k not divisible by 7, k is a cube in 7-adic field if and only if k == 1, 6 (mod 13). If k is a cube in 7-adic field, then k has exactly three cubic roots.
LINKS
Wikipedia, p-adic number
FORMULA
Equals A319297*(A212152-1) = A319297*A212152^2, where each A-number represents a 7-adic number.
Equals A319305*(A212155-1) = 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
Digits of p-adic cubic roots:
A290566 (5-adic, 2^(1/3));
A290563 (5-adic, 3^(1/3));
A309443 (5-adic, 4^(1/3));
A319297, A319305, this sequence (7-adic, 6^(1/3));
A321106, A321107, A321108 (13-adic, 5^(1/3)).
Sequence in context: A106333 A104748 A117335 * A244980 A367311 A021863
KEYWORD
nonn,base
AUTHOR
Jianing Song, Aug 27 2019
STATUS
approved