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

0,1

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.

Links

Table of n, a(n) for n=0..87.

Wikipedia, p-adic number

Formula

Equals A325489*A210851 = A325492*A210850.

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

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

Example

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.

Prog

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

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)).

Sequence in context: A127375 A238573 A346965 * A195084 A306803 A319974

Adjacent sequences: A325488 A325489 A325490 * A325492 A325493 A325494

Keyword

nonn,base

Author

Jianing Song, Sep 07 2019

Status

approved