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

1,1

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.

Links

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

Example

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.

Mathematica

Table[If[Prime[n]<6Ceiling[Prime[n]/6]+3<Prime[n+1] || Prime[n]<6Floor[Prime[n]/6]+3<Prime[n+1] , 1, 0], {n, 105}] (* James C. McMahon, Jan 29 2024 *)

Prog

(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

Crossrefs

Same as A100810 after first term.

Sequence in context: A361496 A360125 A324883 * A341612 A252742 A066247

Adjacent sequences: A105999 A106000 A106001 * A106003 A106004 A106005

Keyword

easy,nonn

Author

Giovanni Teofilatto, Apr 29 2005

Extensions

Edited by Ray Chandler, Oct 17 2006

Status

approved