A275022 Primes not in A001097 and not in A275021 that occur in pairs of the form {p, p+6}.

47, 53, 251, 257, 331, 337, 353, 359, 367, 373, 541, 547, 557, 563, 587, 593, 607, 613, 647, 653, 727, 733, 947, 953, 977, 983, 991, 997, 1097, 1103, 1117, 1123, 1181, 1187, 1361, 1367, 1433, 1439, 1493, 1499, 1657, 1663, 1741, 1747, 1753

Offset

1,1

Comments

List of prime numbers that occur in pairs of the form {p, p+6} after the sequential removal, from a list of all the primes, of (1) the one pair of primes of the form {p, p+1}, (2) all remaining twin prime pairs {p, p+2}, and (3) all remaining pairs of the form {p, p+4}.

Conjecture: The sequence has infinitely many terms and the sum of their reciprocals converges.

Links

Table of n, a(n) for n=1..45.

Prog

(PARI) {
/* For biggest n allocatemem(max)*/
n=10^4-1;
v=vector(n, unused, 1);
for(i=2, sqrt(n),
    if(v[i],
       forstep(j=i^2, n, i, v[j]=0))
      );
v[2]=0; v[3]=0;
for(i=5, n-2,
     if(v[i]&&v[i+2],
        v[i]=0; v[i+2]=0
       )
    );
for(i=5, n-4,
     if(v[i]&&v[i+4],
        v[i]=0; v[i+4]=0;
       )
    );
for(i=5, n-6,
     if(v[i]&&v[i+6],
        print1(i", "i+6", ");
        v[i]=0; v[i+6]=0;
       )
    )
}

Crossrefs

Cf. A001097, A275021.

Sequence in context: A141279 A155139 A106279 * A355601 A048581 A169716

Adjacent sequences: A275019 A275020 A275021 * A275023 A275024 A275025

Keyword

nonn,more

Author

Dimitris Valianatos, Nov 12 2016

Status

approved