A088150 Value of n-th digit (counting from the right) in binary representation of n^n.

1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1

Offset: 0

Author

Reinhard Zumkeller, Sep 20 2003

Keywords

• nonn
• base

Comments

a(n)=d(n) with n^n = Sum(d(k)*2^k: 0<=d(k)<2, k>=0).

Examples

			n=5, 5^5=3125 -> '110000110101', '1100001-----': a(5)=1.
		

Links

• Eric Weisstein's World of Mathematics, Binary

Crossrefs

Cf. A007088, A000312, A088151, A088152, A088153, A088154, A088155, A088156, A088157.

Programs

Mathematica

Join[{1,0},Table[IntegerDigits[n^n,2][[-n-1]],{n,2,110}]] (* Harvey P. Dale, Oct 14 2021 *)

Formula

a(n) = floor(n^n / 2^n) mod 2.

Extensions

Definition clarified by Harvey P. Dale, Oct 14 2021