A080545 Characteristic function of {1} union {odd primes}: 1 if n is 1 or an odd prime, else 0.

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

Offset: 1

Author

N. J. A. Sloane, Mar 21 2003

Keywords

• nonn
• easy

Examples

			a(2) = 0 because 2 is prime but even.
a(3) = 1 because 3 is prime and odd. Likewise for a(5) and a(7).
a(4) = 0 because 4 is neither prime nor odd. Likewise for a(6) and a(8).
a(9) = 0 because 9 is odd but composite.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1001
• Index entries for characteristic functions

Crossrefs

Cf. A010051, A080355, A080567, A171387.

Differs from A080339 only at a(2).

Programs

Mathematica

Table[Boole[PrimeOmega[n] < 2 && OddQ[n]], {n, 100}] (* Alonso del Arte, Nov 19 2013 *)

Formula

a(n) = (delta(Omega(n), 0) + delta(Omega(n), 1)) * d_0(n), where delta is the Kronecker delta function, Omega is the number of prime factors function (counted with multiplicity), and d_0(n) is the least significant digit of n in binary. - Alonso del Arte, Nov 19 2013

Extensions

Added missing a(2) - Walter Roscello, Nov 19 2013