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

%I #38 Jan 13 2024 10:54:16

%S 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,

%T 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,

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

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

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

%H Paolo Xausa, <a href="/A365689/b365689.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1).

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

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

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

%t PadRight[{},100,{0,1,2,1,4,5,6,1,8,1}] (* _Paolo Xausa_, Oct 16 2023 *)

%o (PARI) a(n) = lift(Mod(n, 10)^((n+1)^(n+2))); \\ _Michel Marcus_, Sep 16 2023

%o (Python)

%o def A365689(n): return pow(n,(n+1)**(n+2),10) # _Chai Wah Wu_, Sep 22 2023

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

%K nonn,base,easy

%O 0,3

%A _Marco RipĂ _, Sep 16 2023