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

0,1

Comments

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

Links

Table of n, a(n) for n=0..101.

Eric Weisstein's World of Mathematics, Binary

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A204418 A127245 A175192 * A365938 A117567 A307183

Adjacent sequences: A088147 A088148 A088149 * A088151 A088152 A088153

Keyword

nonn,base

Author

Reinhard Zumkeller, Sep 20 2003

Extensions

Definition clarified by Harvey P. Dale, Oct 14 2021

Status

approved