A324087 Digits of one of the four 3-adic integers 3^(1/4) that is congruent to 10 mod 13.

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

Offset

0,1

Comments

One of the two square roots of A322088, where an A-number represents a 13-adic number. The other square root is A324086.

For k not divisible by 13, k is a fourth power in 13-adic field if and only if k == 1, 3, 9 (mod 13). If k is a fourth power in 13-adic field, then k has exactly 4 fourth-power roots.

Links

Table of n, a(n) for n=0..80.

Wikipedia, p-adic number

Formula

Equals A324085*A286838 = A324153*A286839.

a(n) = (A324083(n+1) - A324083(n))/13^n.

For n > 0, a(n) = 12 - A324086(n).

Example

The unique number k in [1, 13^3] and congruent to 10 modulo 13 such that k^4 - 3 is divisible by 13^3 is k = 1622 = (97A)_13, so the first three terms are 10, 7 and 9.

Prog

(PARI) a(n) = lift(-sqrtn(3+O(13^(n+1)), 4))\13^n

Crossrefs

Cf. A286838, A286839, A322087, A324077, A324082, A324083, A324084, A324085, A324086, A324153.

Sequence in context: A343551 A098592 A016731 * A068444 A210285 A190996

Adjacent sequences: A324084 A324085 A324086 * A324088 A324089 A324090

Keyword

nonn,base

Author

Jianing Song, Sep 01 2019

Status

approved