A132194 a(n) = 1 if n-th prime is 0 or 2 mod 3, otherwise 0.

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

Offset: 1

Author

Roger L. Bagula, Nov 05 2007

Keywords

• nonn
• easy

Comments

Equivalently, a(n) = 0 if n-th prime is 1 mod 3, otherwise 1. - Wouter Meeussen, May 21 2019

Binary sequence based on the primes: play it at a slower tempo to appreciate the irregularities.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for characteristic functions.

Crossrefs

Characteristic function of A133677.

Cf. A039701, A130198, A099618.

Programs

Magma

[(NthPrime(n) mod 3) eq 1 select 0 else 1: n in [1..200]]; // G. C. Greubel, May 21 2019

Maple

a := n -> 1 - irem(modp(ithprime(n), 3), 2):
seq(a(n), n = 1..105); # Peter Luschny, May 21 2019

Mathematica

Table[If[Mod[Prime[n],3]== 1,0,1],{n,200}] (* Harvey P. Dale, May 21 2019 *)

PARI

{a(n) = if(prime(n)%3==1, 0, 1)}; \\ G. C. Greubel, May 21 2019

Sage

def a(n):
    if (mod(nth_prime(n), 3)==1): return 0
    else: return 1
[a(n) for n in (1..200)] # G. C. Greubel, May 21 2019

Formula

a(n) = 1-A099618(n). - R. J. Mathar, Jun 06 2019

Sum_{k=1..n} a(k) ~ n / 2. - Amiram Eldar, Mar 14 2025

Extensions

Definition corrected by Harvey P. Dale, May 21 2019