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

0,3

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).

Links

Table of n, a(n) for n=0..86.

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).

Formula

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

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A019981 A194281 A117038 * A172168 A371874 A321095

Adjacent sequences: A365932 A365933 A365934 * A365936 A365937 A365938

Keyword

nonn,base,easy

Author

Marco Ripà, Sep 23 2023

Status

approved