A179081 Parity of sum of digits of n.

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

Offset: 0

Author

Reinhard Zumkeller, Jun 28 2010

Keywords

• base
• nonn

Comments

a(n) = A000035(A007953(n));

characteristic function of numbers with an odd sum of digits in their decimal representation:

a(A054684(n)) = 1; a(A054683(n)) = 0;

a(A179083(n)) = a(A179085(n)) = 1;

a(A179082(n)) = a(A179084(n)) = 0.

Examples

			a(789) = (7+8+9) mod 2 = 0;
a(790) = (7+9+0) mod 2 = 0;
a(791) = (7+9+1) mod 2 = 1.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for characteristic functions

Programs

Mathematica

Array[Mod[Total[IntegerDigits[#]],2]&,110,0] (* Harvey P. Dale, Feb 20 2013 *)

PARI

a(n) = vecsum(digits(n)) % 2 \\ Jeppe Stig Nielsen, Jan 06 2018

Formula

a(n) = if n<10 then (n mod 2) else a([n/10]) XOR (n mod 2).