The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A275021 Pairs of primes p, p+4 such that p-2 and p+6 are composite. 2
 79, 83, 127, 131, 163, 167, 379, 383, 397, 401, 439, 443, 487, 491, 499, 503, 673, 677, 739, 743, 757, 761, 769, 773, 907, 911, 937, 941, 967, 971, 1009, 1013, 1213, 1217, 1549, 1553, 1567, 1571, 1579, 1583, 1597, 1601, 2203, 2207, 2293, 2297 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS List of prime numbers that occur in pairs of the form {p, p+4} 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}. Conjecture: the sequence has infinitely many terms and the sum of their reciprocals converges. The second half of the conjecture is correct. The first half is true on Dickson's conjecture (because, for example, it would show that there are infinitely many k such that 210k+127 and 210k+131 are both prime). - Charles R Greathouse IV, Nov 20 2016 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 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],         print1(i", "i+4", ");         v[i]=0; v[i+4]=0;        )     ) } (PARI) p=2; q=3; r=5; forprime(s=7, 1e3, if(r-q==4 && q-p>2 && s-r>2, print1(q", "r", ")); p=q; q=r; r=s) \\ Charles R Greathouse IV, Nov 19 2016 CROSSREFS Cf. A001097, A007510. Sequence in context: A051326 A033399 A272639 * A033251 A015984 A235227 Adjacent sequences:  A275018 A275019 A275020 * A275022 A275023 A275024 KEYWORD nonn,easy AUTHOR Dimitris Valianatos, Nov 12 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 28 09:36 EDT 2021. Contains 346325 sequences. (Running on oeis4.)