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

Author

Marco Ripà, Sep 16 2023

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

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

Formula

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

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