A088153 a(n) is the value of the n-th digit in the decimal representation of n^n.

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

Offset: 0

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

• nonn
• base

Comments

a(n) = d(n) with n^n = Sum_{0<=d(k)<10, k>=0} d(k)*10^k.

Examples

			For n=16, 16^16 = 18446744073709551616, a(16)=4.
a(0)=1, a(k)=0 for 0 < k < 10 and a(10)=1.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Decimal

Crossrefs

Cf. A000312, A088150, A088151, A088152, A088154, A088155, A088156, A088157.

Programs

Maple

f:= proc(n) local x, L;
   x:= n &^ n mod 10^(n+1);
   floor(x/10^n)
end proc:
f(0):= 1:
map(f, [$0..101]); # Robert Israel, Dec 02 2022

Formula

a(n) = floor(n^n / 10^n) mod 10.