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

0,3

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.

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(Python)
from sympy import isprime
def A370482(n): return isprime(n)+(n&1^1) # Chai Wah Wu, Apr 25 2024
(PARI) A370482(n) = (!(n%2) + isprime(n)); \\ Antti Karttunen, Jan 17 2025

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

Sequence in context: A037910 A162781 A056975 * A294079 A375669 A114117

Adjacent sequences: A370479 A370480 A370481 * A370483 A370484 A370485

Keyword

nonn,easy

Author

Jens Ahlström, Mar 31 2024

Status

approved