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

Author

Jianing Song, Sep 01 2019

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Wikipedia, p-adic number

Crossrefs

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

Programs

PARI

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

Formula

Equals A324085*A286839 = A324153*A286838.

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

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