A106002 a(n)=1 if there is a number of the form 6k+3 such that prime(n) < 6k+3 < prime(n+1), otherwise 0.

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

Offset: 1

Author

Giovanni Teofilatto, Apr 29 2005

Keywords

• easy
• nonn

Comments

Except for first two primes and twin primes, there is always at least one number of the form 6k+3 between two successive primes.

Examples

			a(3)=0 because between prime(3)=5 and prime(4)=7 there are no numbers of the form 6k+3;
a(4)=1 because between prime(4)=7 and prime(5)=11 there is 9=6*1+3.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Same as A100810 after first term.

Programs

Mathematica

Table[If[Prime[n]<6Ceiling[Prime[n]/6]+3James C. McMahon, Jan 29 2024 *)

PARI

a(n) = my(p=prime(n)); for(k=p+1, nextprime(p+1)-1, if (!((k-3) % 6), return(1))); \\ Michel Marcus, Jan 30 2024

Python

from sympy import sieve
def A106002(n):
    for comp in range(sieve[n]+1, sieve[n+1]):
        if (comp-3) % 6 == 0: return 1
    return 0 # Karl-Heinz Hofmann, Jan 30 2024

Extensions

Edited by Ray Chandler, Oct 17 2006