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 A275022 Primes not in A001097 and not in A275021 that occur in pairs of the form {p, p+6}. 0
 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 (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+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 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 * A048581 A169716 A045140 Adjacent sequences:  A275019 A275020 A275021 * A275023 A275024 A275025 KEYWORD nonn,more AUTHOR Dimitris Valianatos, Nov 12 2016 STATUS approved

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Last modified February 28 22:52 EST 2020. Contains 332336 sequences. (Running on oeis4.)