A324086 Digits of one of the four 3-adic integers 3^(1/4) that is congruent to 3 mod 13.

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

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 A324087.

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*A286839 = A324153*A286838.

a(n) = (A324082(n+1) - A324082(n))/13^n.

For n > 0, a(n) = 12 - A324087(n).

Example

The unique number k in [1, 13^3] and congruent to 3 modulo 13 such that k^4 - 3 is divisible by 13^3 is k = 575 = (353)_13, so the first three terms are 3, 5 and 3.

Prog

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

Crossrefs

Cf. A286838, A286839, A322087, A324077, A324082, A324083, A324084, A324085, A324087, A324153.

Sequence in context: A134429 A100667 A329736 * A286108 A096438 A299418

Adjacent sequences: A324083 A324084 A324085 * A324087 A324088 A324089

Keyword

nonn,base

Author

Jianing Song, Sep 01 2019

Status

approved