A365935 -id:A365935 - cp's OEIS frontend

A365707 Initial digit of n^(n+1) (A007778(n)).

0, 1, 8, 8, 1, 1, 2, 5, 1, 3, 1, 3, 1, 3, 1, 6, 2, 1, 7, 3, 2, 1, 7, 4, 3, 2, 1, 1, 9, 7, 6, 5, 4, 4, 3, 3, 3, 3, 4, 4, 4, 5, 6, 7, 9, 1, 1, 1, 2, 3, 4, 6, 8, 1, 1, 2, 4, 6, 1, 1, 2, 4, 8, 1, 2, 4, 8, 1, 2, 5, 1, 1, 3, 7, 1, 3, 6, 1, 2, 6, 1, 3, 7, 1, 3, 8, 2

Offset: 0

Marco Ripà, Sep 16 2023

			a(3) = 8, since 3^(3+1) = 3^4 = 81.

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A000030, A007778, A061505, A138029, A364855, A365935.

seq(convert(n^(n+1),base,10)[-1],n=0..100); # Robert Israel, Feb 16 2024

Join[{0}, Table[Floor[n^(n+1)/10^Floor[Log10[n^(n+1)]]], {n, 86}]]

a(n) = floor((n^(n+1))/10^floor(log_10(n^(n+1)))).

a(n) = A000030(A007778(n)).

A365936 Final digit (in decimal system) of n^(n-1) = A000169(n).

Original entry on oeis.org

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

Offset: 1

Marco Ripà, Sep 23 2023

This is a periodic sequence with period 20 which is twice the considered radix.

			For n = 4, a(4) = 4^3 mod 10 = 64 mod 10 = 4.

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).

Cf. A000169, A056849, A120962, A138029, A365707.

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

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

a(n) = A365935(n+10).

cp's OEIS Frontend

A365707 Initial digit of n^(n+1) (A007778(n)).

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