A080339 Characteristic function of {1} union {primes}: 1 if n is 1 or a prime, else 0.

1, 1, 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

Comments

Characteristic function of noncomposite numbers (see A008578). - Omar E. Pol, Oct 07 2013

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Aminu Alhaji Ibrahim, Sa’idu Isah Abubaka, Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties, Advances in Pure Mathematics, 2016, 6, 409-419.

Eric Weisstein's World of Mathematics, Prime Formulas

Index entries for characteristic functions

Formula

a(1)=1, and a(n) = Prod_{k=1...n-1}(k/n)^2 where (a/b) is the Jacobi symbol and n>1. - Dimitri Papadopoulos, Jan 13 2016

Maple

1, seq(`if`(isprime(i), 1, 0), i=2..100); # Robert Israel, Jan 11 2016

Mathematica

Table[Which[n == 1, 1, PrimeQ[n], 1, True, 0], {n, 110}] (* Harvey P. Dale, Oct 03 2011 *)
Table[Boole[PrimeOmega[n] < 2], {n, 100}] (* Alonso del Arte, Nov 19 2013 *)

Prog

(PARI) a(n) = (n==1) + isprime(n); \\ Michel Marcus, Jan 13 2016

Crossrefs

Cf. A010051, A080355.

Cf. A036234 (partial sums).

Sequence in context: A187036 A192490 A267133 * A294905 A353787 A297086

Adjacent sequences: A080336 A080337 A080338 * A080340 A080341 A080342

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Mar 21 2003

Status

approved