A365689 Final decimal digit of n^((n+1)^(n+2)) = A030198(n).

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

Offset

0,3

Comments

Period 10, repeat: [0, 1, 2, 1, 4, 5, 6, 1, 8, 1].

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = n^((n+1)^(n+2)) mod 10.

a(n) = A103562(n) for n >= 4 (as 3^(2^1) == 9 (mod 10) instead of 1).

Example

For n = 2, a(2) = 2417851639229258349412352 mod 10 = 2.

Mathematica

PadRight[{}, 100, {0, 1, 2, 1, 4, 5, 6, 1, 8, 1}] (* Paolo Xausa, Oct 16 2023 *)

Prog

(PARI) a(n) = lift(Mod(n, 10)^((n+1)^(n+2))); \\ Michel Marcus, Sep 16 2023
(Python)
def A365689(n): return pow(n, (n+1)**(n+2), 10) # Chai Wah Wu, Sep 22 2023

Crossrefs

Cf. A030198, A103562, A120962, A365689 (initial digit).

Sequence in context: A075423 A144774 A326056 * A373948 A074720 A323456

Adjacent sequences: A365686 A365687 A365688 * A365690 A365691 A365692

Keyword

nonn,base,easy

Author

Marco Ripà, Sep 16 2023

Status

approved