A370482 Characteristic function of primes plus characteristic function of even numbers.

1, 0, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1

Offset: 0

Author

Jens Ahlström, Mar 31 2024

Keywords

• nonn
• easy

Comments

There is only one 2 in the sequence, so if the value 2 is blanked out, a riddle is created that demands some out-of-the-box thinking.

Examples

			1 is neither prime nor even so a(1) = 0 + 0 = 0.
2 is both a prime and even so a(2) = 1 + 1 = 2.
3 is a prime but odd so a(3) = 1 + 0 = 1.
4 is not a prime but even so a(4) = 0 + 1 = 1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..100000

Crossrefs

Cf. A010051, A059841.

If a(2) were 1 instead of 2, then this would the characteristic function of {0} U A106092, whose complement A014076 gives the positions of 0's. - Antti Karttunen, Jan 17 2025

Programs

Mathematica

a[n_] := Boole[PrimeQ[n]] + Boole[EvenQ[n]]; Array[a, 100, 0] (* Amiram Eldar, Mar 31 2024 *)

PARI

A370482(n) = (!(n%2) + isprime(n)); \\ Antti Karttunen, Jan 17 2025

Python

from sympy import isprime
def A370482(n): return isprime(n)+(n&1^1) # Chai Wah Wu, Apr 25 2024

Formula

a(n) = A010051(n) + A059841(n).