A325491 Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 3 mod 5.

3, 0, 4, 1, 4, 2, 4, 0, 4, 1, 4, 2, 2, 2, 3, 2, 3, 0, 4, 1, 0, 2, 3, 0, 3, 3, 2, 4, 4, 1, 4, 3, 3, 1, 3, 0, 0, 4, 2, 0, 4, 0, 3, 2, 4, 3, 2, 1, 2, 0, 2, 0, 3, 1, 4, 2, 3, 4, 1, 1, 1, 1, 4, 2, 2, 1, 3, 3, 0, 3, 3, 4, 3, 0, 4, 1, 1, 1, 4, 1, 4, 4, 0, 4, 1, 2, 1, 3

Offset: 0

Author

Jianing Song, Sep 07 2019

Keywords

• nonn
• base

Comments

One of the two square roots of A324026, where an A-number represents a 5-adic number. The other square root is A325490.

For k not divisible by 5, k is a fourth power in 5-adic field if and only if k == 1 (mod 5). If k is a fourth power in 5-adic field, then k has exactly 4 fourth-power roots.

Examples

			The unique number k in [1, 5^3] and congruent to 3 modulo 5 such that k^4 - 6 is divisible by 5^3 is k = 103 = (403)_5, so the first three terms are 3, 0 and 4.
		

Links

• Wikipedia, p-adic number

Crossrefs

Cf. A210850, A210851, A324026, A325484, A325485, A325486, A325487.

Digits of p-adic fourth-power roots:

A325489, A325490, this sequence, A325492 (5-adic, 6^(1/4));

A324085, A324086, A324087, A324153 (13-adic, 3^(1/4)).

Programs

PARI

a(n) = lift(-sqrtn(6+O(5^(n+1)), 4) * sqrt(-1+O(5^(n+1))))\5^n

Formula

Equals A325489*A210851 = A325492*A210850.

a(n) = (A325486(n+1) - A325486(n))/13^n.

For n > 0, a(n) = 4 - A325490(n).