A365935 Final digit (in decimal system) of n^(n+1) = A007778(n).

0, 1, 8, 1, 4, 5, 6, 1, 8, 1, 0, 1, 2, 9, 4, 5, 6, 9, 2, 1, 0, 1, 8, 1, 4, 5, 6, 1, 8, 1, 0, 1, 2, 9, 4, 5, 6, 9, 2, 1, 0, 1, 8, 1, 4, 5, 6, 1, 8, 1, 0, 1, 2, 9, 4, 5, 6, 9, 2, 1, 0, 1, 8, 1, 4, 5, 6, 1, 8, 1, 0, 1, 2, 9, 4, 5, 6, 9, 2, 1, 0, 1, 8, 1, 4, 5, 6

Offset: 0

Author

Marco Ripà, Sep 23 2023

Keywords

• nonn
• base
• easy

Comments

This is a periodic sequence (1, 8, 1, 4, 5, 6, 1, 8, 1, 0, 1, 2, 9, 4, 5, 6, 9, 2, 1, 0) with period 20 (which is twice the base).

Examples

			For n = 3, a(3) = 3^4 mod 10 = 81 mod 10 = 1.
		

Links

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

Crossrefs

Cf. A007778, A010879, A056849, A120962, A365707.

Programs

Mathematica

a[n_]:=Last[IntegerDigits[n^(n+1)]]; Array[a,87,0] (* Stefano Spezia, Sep 26 2023 *)

PARI

a(n) = lift(Mod(n, 10)^(n+1)); \\ Michel Marcus, Sep 23 2023

Formula

a(n) = n^(n+1) mod 10.

a(n) = A010879(A007778(n)).

a(n) = A365936(n+10).