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

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..1001

Index entries for characteristic functions

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

Example

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.

Mathematica

Table[Boole[PrimeOmega[n] < 2 && OddQ[n]], {n, 100}] (* Alonso del Arte, Nov 19 2013 *)
Table[Which[n==1, 1, PrimeQ[n]&&OddQ[n], 1, True, 0], {n, 120}] (* Harvey P. Dale, Feb 02 2026 *)

Crossrefs

Cf. A010051, A080355, A080567, A171387.

Differs from A080339 only at a(2).

Sequence in context: A286046 A189215 A285128 * A355820 A374367 A099991

Adjacent sequences: A080542 A080543 A080544 * A080546 A080547 A080548

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 21 2003

Extensions

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

Status

approved