A325490 Digits of one of the four 5-adic integers 6^(1/4) that is congruent to 2 mod 5.

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

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 A325491.

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

Robert Israel, Table of n, a(n) for n = 0..10000

Wikipedia, p-adic number

Formula

Equals A325489*A210850 = A325492*A210851.

a(n) = (A325485(n+1) - A325485(n))/13^n.

For n > 0, a(n) = 4 - A325491(n).

Example

The unique number k in [1, 5^3] and congruent to 2 modulo 5 such that k^4 - 6 is divisible by 5^3 is k = 22 = (42)_5, so the first three terms are 2, 4 and 0.

Maple

S:= select(t -> op([1, 3, 1], t)=2, [padic:-rootp(_Z^4-6, 5, 100)]):
op([1, 1, 3], S); # Robert Israel, Mar 23 2023

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, this sequence, A325491, A325492 (5-adic, 6^(1/4));

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

Sequence in context: A007631 A281765 A155517 * A123514 A064178 A018220

Adjacent sequences: A325487 A325488 A325489 * A325491 A325492 A325493

Keyword

nonn,base

Author

Jianing Song, Sep 07 2019

Status

approved