A373098 Last digit of n*2^n.

0, 2, 8, 4, 4, 0, 4, 6, 8, 8, 0, 8, 2, 6, 6, 0, 6, 4, 2, 2, 0, 2, 8, 4, 4, 0, 4, 6, 8, 8, 0, 8, 2, 6, 6, 0, 6, 4, 2, 2, 0, 2, 8, 4, 4, 0, 4, 6, 8, 8, 0, 8, 2, 6, 6, 0, 6, 4, 2, 2, 0, 2, 8, 4, 4, 0, 4, 6, 8, 8, 0, 8, 2, 6, 6, 0, 6, 4, 2, 2, 0, 2, 8, 4, 4, 0, 4, 6, 8, 8, 0, 8, 2, 6, 6, 0, 6, 4, 2, 2

Offset: 0

Author

Javier Rodríguez Ríos, May 23 2024

Keywords

• nonn
• base
• easy

Comments

Periodic with period 20: [0,2,8,4,4,0,4,6,8,8,0,8,2,6,6,0,6,4,2,2].

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,1,1,-1,-1,1,0,-1,0,1).

Crossrefs

Cf. A010879, A036289.

Cf. A373099, A373100.

Programs

Maple

a:= n-> n*2&^n mod 10:
seq(a(n), n=0..100);

Mathematica

a[n_] := Mod[n*2^n, 10]

PARI

a(n,b=10) = lift(n*Mod(2,b)^n) \\ Hugo Pfoertner, May 24 2024

Python

def a(n):
    return (n * 2**n) % 10

Formula

a(n) = A010879(A036289(n)).

a(n) = A373099(n) - 1.

a(n) = A373100(n) + 1 (n >= 1).

a(n) = 0 if n mod 5 = 0,

2 if n mod 20 = {1, 12, 18, 19},

8 if n mod 20 = {2, 8, 9, 11},

4 if n mod 20 = {3, 4, 6, 17},

6 if n mod 20 = {7, 13, 14, 16}.