This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A128467 #20 Oct 09 2023 11:19:40 %S A128467 11,41,71,101,131,161,191,221,251,281,311,341,371,401,431,461,491,521, %T A128467 551,581,611,641,671,701,731,761,791,821,851,881,911,941,971,1001, %U A128467 1031,1061,1091,1121,1151,1181,1211,1241,1271,1301,1331,1361,1391,1421,1451 %N A128467 a(n) = 30*n + 11. %C A128467 Possible lower bounds of twin primes pairs ending in 1. %C A128467 For a 30k+r "wheel", r = 11, 17, 29 are the only possible values that can form a lower twin prime pair. The 30k + r wheel gives the recurrence 1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, ... which is frequently used in prime number sieves to skip multiples of 2, 3, 5. The fact that adding 2 to 30k + 1, 7, 13, 19, 23 will give us a multiple of 3 or 5 precludes these numbers from being a lower member of a twin prime pair. This leaves us with r = 11, 17, 29 as the only possible cases to form a lower bound of a twin prime pair. %F A128467 From _R. J. Mathar_, Dec 05 2007: (Start) %F A128467 O.g.f.: (11+19*x)/(-1+x)^2 = 19/(-1+x) + 30/(-1+x)^2. %F A128467 a(n) = 30*n + 11. (End) %e A128467 41 = 30*1 + 11, the lower part of the twin prime pair 41,43. %t A128467 Range[11, 7000, 30] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *) %t A128467 30*Range[0,50]+11 (* _Harvey P. Dale_, Oct 09 2023 *) %o A128467 (PARI) forstep(x=11,1500,30,print1(x",")) %K A128467 easy,nonn %O A128467 0,1 %A A128467 _Cino Hilliard_, May 05 2007 %E A128467 Offset corrected by _Eric Rowland_, Aug 15 2017