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Primes not in A001097 and not in A275021 that occur in pairs of the form {p, p+6}.
0

%I #21 Dec 08 2016 10:23:13

%S 47,53,251,257,331,337,353,359,367,373,541,547,557,563,587,593,607,

%T 613,647,653,727,733,947,953,977,983,991,997,1097,1103,1117,1123,1181,

%U 1187,1361,1367,1433,1439,1493,1499,1657,1663,1741,1747,1753

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

%C 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}.

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

%o (PARI) {

%o /* For biggest n allocatemem(max)*/

%o n=10^4-1;

%o v=vector(n, unused, 1);

%o for(i=2, sqrt(n),

%o if(v[i],

%o forstep(j=i^2, n, i, v[j]=0))

%o );

%o v[2]=0; v[3]=0;

%o for(i=5, n-2,

%o if(v[i]&&v[i+2],

%o v[i]=0; v[i+2]=0

%o )

%o );

%o for(i=5, n-4,

%o if(v[i]&&v[i+4],

%o v[i]=0; v[i+4]=0;

%o )

%o );

%o for(i=5, n-6,

%o if(v[i]&&v[i+6],

%o print1(i", "i+6", ");

%o v[i]=0; v[i+6]=0;

%o )

%o )

%o }

%Y Cf. A001097, A275021.

%K nonn,more

%O 1,1

%A _Dimitris Valianatos_, Nov 12 2016